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N_00 audio cassettes and N_01 video cassettes cost rs N_02 , while N_03 audio cassettes and N_04 video cassettes cost rs N_05 . Find the cost of an audio cassette and a video cassette. | N_00 * v0 + N_01 * v1 = N_02 <BRG> N_03 * v0 + N_04 * v1 = N_05 | 30.0 300.0 | 7.0 3.0 1110.0 5.0 4.0 1350.0 |
Tickets cost N_00 dollars for students, and N_01 dollars for general admission. You sell N_02 tickets and collect N_03 dollars. How many student tickets did you sell, and how many general admission tickets did you sell? | N_00 * v0 + N_01 * v1 = N_03 <BRG> v0 + v1 = N_02 | 137.0 388.0 | 4.0 6.0 525.0 2876.0 |
N_00 is divided into two parts such that N_01 times the first part added to N_02 times the second part makes N_03 . Find each part. | N_01 * v0 + N_02 * v1 = N_03 <BRG> v0 + v1 = N_00 | 13.0 11.0 | 24.0 7.0 5.0 146.0 |
It takes a boat N_00 hours to travel N_01 miles down a river and N_02 hours to return upstream to its starting point. What is the rate of the current in the river? | N_00 * v0 + N_00 * v1 = N_01 <BRG> N_02 * v0 - N_02 * v1 = N_01 | 1.0 5.0 | 4.0 24.0 6.0 |
N_02 teams of scientists leave a university at the same time in special vans to search for tornadoes. The N_00 st team travels east at N_01 miles per hour, and the N_02 nd team travels west at N_03 miles per hour. their radios have a range of N_04 miles. How much time will pass before the scientists lose radio contact? | N_01 * v0 + N_03 * v0 = N_04 | 2.5 | 1.0 20.0 2.0 30.0 125.0 |
Two cars leave the same point, traveling in opposite directions. One travels at a constant speed of N_00 miles per hour, and the other travels at a constant speed of N_01 miles per hour. In how many hours will they be N_02 miles apart? | N_00 * v0 + N_01 * v0 = N_02 | 3.5 | 52.0 58.0 385.0 |
A N_00 -inch pipe is cut into two pieces. One piece is two times the length of the other. Find the lengths of the two pieces. | v0 + v1 = N_00 <BRG> v1 - 2.0 * v0 = 0.0 | 59.0 118.0 | 177.0 |
To buy both a new car and a new house, Tina sought two loans totaling N_00 dollars. The simple interest rate on the first loan was N_01 , while the simple interest rate on the second loan was N_02 . At the end of the first year, Tina paid a combined interest payment of N_03 dollars. What were the amounts of the two loans? | 0.01 * N_01* v0 + 0.01 * N_02 * v1 = N_00 <BRG> v1 + v0 = N_03 | 8698.95652 309639.04347 | 318.0 0.024 0.047 14.0 |
Mary can purchase roses and daisies from a flower shop. She can buy four roses and five daisies for N_00 dollars or two roses and six daisies for N_01 dollars. What is the individual cost for each rose and daisy? | 4.0 * v0 + 5.0 * v1 = N_00 <BRG> 2.0 * v0 + 6.0 * v1 = N_01 | 1.35 0.5 | 7.9 5.7 |
With a tailwind, a jet flew N_00 miles in N_01 hours. The jet's return trip against the same wind required N_02 hours. Find the jet's speed and the wind speed. | N_01 * v0 + N_01 * v1 = N_00 <BRG> N_02 * v0 - N_02 * v1 = N_00 | 450.0 50.0 | 2000.0 4.0 5.0 |
A furniture dealer has N_00 tables. Some tables have N_03 legs, and some have N_01 legs, but she doesn't know how many of each kind there are. She has counted N_02 legs in total. How many N_03 legged tables are there? | N_03 * v0 + N_01 * v1 = N_02 <BRG> v0 + v1 = N_00 | 16.0 20.0 | 36.0 3.0 124.0 4.0 |
You are making N_00 tons of concrete that are N_01 cement by mixing a N_02 cement mixture with an N_03 cement mixture. How much of the N_03 cement mixture must you use? Answer in units of tons. | N_02 * v0 + N_03 * v1 = N_00 * N_01 <BRG> v0 + v1 = N_00 | 7.0 3.0 | 10.0 0.62 0.2 0.8 |
N_00 is divided into two parts such that N_01 times the first part added to N_02 times the second part makes N_03 . What is the first part? | N_01 * v0 + N_02 * v1 = N_03 <BRG> v0 + v1 = N_00 | 13.0 11.0 | 24.0 7.0 5.0 146.0 |
At Al's Rent-a-Center, it costs N_00 dollars more per month to rent a leather couch than it does to rent a microfiber couch. Pauline rented a leather couch for N_01 months and then exchanged it for a microfiber couch, which she rented for N_02 months. She paid a total of N_03 dollars to rent these couches. Solve this system of equations to find the monthly rental charge for the leather couch in dollars. Find the monthly rental charge for the microfiber couch. | N_01 * v0 + N_02 * v1 = N_03 <BRG> v0 - v1 = N_00 | 99.0 69.0 | 30.0 8.0 12.0 1620.0 |
The larger of two numbers is N_00 less than twice the smaller. The sum of the two numbers is N_01 . Find the two numbers. | 2.0 * v0 - v1 = N_00 <BRG> v0 + v1 = N_01 | 31.0 39.0 | 23.0 70.0 |
N_00 of Joe's income each month goes to taxes. If she pays N_01 dollars in taxes each month, what is her monthly income in dollars? | N_00 * v0 = N_01 | 2120.0 | 0.4 848.0 |
A plane flying with a tailwind flew at a speed of N_00 miles per hour, relative to the ground. When flying against the tailwind, it flew at a speed of N_01 miles per hour. Find the speed of the tailwind. | v0 + v1 = N_00 <BRG> v0 - v1 = N_01 | 75.0 385.0 | 460.0 310.0 |
A student is pricing N_04 different picture packages. John's Photo World charges N_00 dollars per sheet and a one-time sitting fee of N_01 dollars. Sam's Picture Emporium charges N_02 dollars per sheet and a one-time sitting fee of N_03 dollars. For how many sheets of pictures do the N_04 companies charge the same amount? | N_00 * v0 - N_02 * v0 = N_03 - N_01 | 12.0 | 2.75 125.0 1.5 140.0 2.0 |
A baseball player has a batting average of N_00 with N_01 hits in N_02 bats. His average against left-handed pitching is N_03 . Against right-handed pitching, it is N_04 . How many times did he bat against left-handers? | N_04 * v0 + N_03 * v1 = N_01 <BRG> v0 + v1 = N_02 | 180.0 420.0 | 0.32 192.0 600.0 0.25 0.35 |
Two mechanics worked on a car. The first mechanic charged N_00 dollars per hour, and the second mechanic charged N_01 dollars per hour. The mechanics worked for a combined total of N_02 hours, and together they charged a total of N_03 dollars. How long did the first mechanic and second mechanic work? | N_00 * v0 + N_01 * v1 = N_03 <BRG> v0 + v1 = N_02 | 15.0 5.0 | 45.0 85.0 20.0 1100.0 |
Pedro goes to the market and buys a total of N_00 plums and peaches for N_01 dollars. A plum costs N_02 dollars, and a peach costs N_03 dollar. How many plums did Pedro buy? | N_03 * v0 + N_02 * v1 = N_01 <BRG> v0 + v1 = N_00 | 20.0 12.0 | 32.0 52.0 2.0 1.0 |
For a special event at the TCR spring fest, the cost of N_00 adult tickets and N_02 student tickets was N_01 dollars, and the cost of N_02 adult tickets and N_03 student tickets was N_04 dollars. Find the admission price for an adult ticket and for a student ticket at the spring fest in dollars. | N_00 * v0 + N_02 * v1 = N_01 <BRG> N_02 * v0 + N_03 * v1 = N_04 | 8.0 15.0 | 3.0 84.0 4.0 2.0 62.0 |
A boat travels N_00 miles upstream in N_01 hours. The boat travels the same distance downstream in N_02 hours. What is the speed of the boat in still water in miles per hour? What is the speed of the current in miles per hour? | N_02 * v0 + N_02 * v1 = N_00 <BRG> N_01 * v0 - N_01 * v1 = N_00 | 12.0 3.0 | 45.0 5.0 3.0 |
Michael rented a truck for one day. There was a rental fee of N_00 dollars, and there also was a charge of N_01 cents for each mile. Michael paid N_02 dollars when he returned the truck. For how many miles did he drive the truck? | 0.01 * N_01 * v0 = N_02 - N_00 | 299.0 | 20.99 25.0 95.74 |
The sum of the numbers of boys and girls in a class is N_00 . If twice the number of girls exceeds the number of boys by N_01 , find the number of girls in the class. Find the number of boys. | 2.0 * v0 - v1 = N_01 <BRG> v0 + v1 = N_00 | 16.0 20.0 | 36.0 12.0 |
Separate N_00 into N_01 parts so that N_02 of one part exceeds N_03 of the other part by N_04 . What is the smaller part? What is the larger part? | N_02 * v0 - N_03 * v1 = N_04 <BRG> v1 + v0 = N_00 | 16.0 50.0 | 66.0 2.0 0.4 0.625 10.0 |
A garden table and a bench cost N_00 combined. The price of the garden table is two times the price of the bench. What is the cost of the bench? | v0 + v1 = N_00 <BRG> v1 - 2.0 * v0 = 0.0 | 250.0 500.0 | 750.0 |
Lisa invested N_00 dollars, part at N_01 and the rest at N_02 per year. How much did she invest at N_01 and N_02 if her total return per year on the investments was N_03 dollars? | N_01* v0 + N_02 * v1 = N_03 <BRG> v1 + v0 = N_00 | 2000.0 6000.0 | 8000.0 0.04 0.05 380.0 |
To make N_00 kilograms of aluminum alloy with N_01 aluminum, a scientist wants to use two metals with N_03 and N_04 aluminum content respectively. How many kilograms of N_03 aluminum and how many kilograms of N_04 aluminum should she mix? | N_03* v0 + N_04 * v1 = N_00 * N_01 <BRG> v0 + v1 = N_00 | 4.0 6.0 | 10.0 0.6 0.45 0.7 |
N_00 of a certain number is N_01 more than N_02 of a number. Find the number. | N_00 * v0 - N_02 * v0 = N_01 | 30.003 | 0.5 10.0 0.1667 |
The difference between two numbers is N_00 . Find the numbers if their sum is N_01 . | v0 + v1 = N_01 <BRG> v0 - v1 = N_00 | 27.5 18.5 | 9.0 46.0 |
A cosmetologist has a bottle of N_00 hydrogen peroxide solution and a bottle of N_01 hydrogen peroxide solution. The cosmetologist needs N_02 milliliters of a N_03 hydrogen peroxide solution. Find how many milliliters of each solution the cosmetologist needs to mix together. | N_00 * v0 + N_01 * v1 = N_02 * N_03 <BRG> v0 + v1 = N_02 | 100.0 200.0 | 0.07 0.04 300.0 0.05 |
Two times the first number is one more than the second number. If their sum is N_00 , what are the two numbers? | 2.0 * v0 - v1 = 1.0 <BRG> v0 + v1 = N_00 | -21.0 -43.0 | -64.0 |
Eldora and Finn went to an office supply store together. Eldora bought N_00 boxes of paper clips and N_01 packages of index cards for a total cost of N_02 dollars. Finn bought N_03 boxes of paper clips and N_04 packages of index cards for a total cost of N_05 dollars. Find the cost of one box of paper clips and the cost of one package of index cards. | N_03 * v0 + N_04 * v1 = N_05 <BRG> N_00 * v0 + N_01 * v1 = N_02 | 1.85 3.95 | 15.0 7.0 55.4 12.0 10.0 61.7 |
A girl saves N_02 -dollar coins and N_03 -dollar coins. She takes it to a bank, and she has N_00 coins in total that equals N_01 dollars. How many N_02 -dollar coins are there? How many N_03 -dollar coins are there? | N_02 * v0 + N_03 * v1 = N_01 <BRG> v0 + v1 = N_00 | 100.0 80.0 | 180.0 260.0 1.0 2.0 |
In a family, there are N_04 cars. The sum of the average miles per gallon obtained by the two cars in a particular week is N_00 . The first car has consumed N_01 gallons during that week, and the second car has consumed N_02 gallons, for a total of N_03 miles driven by the two cars combined. What was the average gas mileage obtained by each of the N_04 cars that week? | N_01 * v0 + N_02 * v1 = N_03 <BRG> v0 + v1 = N_00 | 25.0 20.0 | 45.0 40.0 20.0 1400.0 2.0 |
The St. Mark's Community Barbecue served N_00 dinners. A child's plate cost N_01 dollars, and an adult's plate cost N_02 dollars. A total of N_03 dollars was collected. How many child's plates were served? How many adult's plates were served? | N_01 * v0 + N_02 * v1 = N_03 <BRG> v0 + v1 = N_00 | 115.0 135.0 | 250.0 3.5 7.0 1347.5 |
On a certain hot summer's day, N_00 people used the public swimming pool. The daily prices are N_01 dollars for children and N_02 dollars for adults. The receipts for admission totaled N_03 dollars. How many children and adults swam at the public pool that day? | N_01 * v0 + N_02 * v1 = N_03 <BRG> v0 + v1 = N_00 | 366.0 388.0 | 754.0 1.5 2.25 1422.0 |
There are N_00 douglas fir and ponderosa pine trees in a section of the forest bought by Sawz logging company. The company paid an average of N_01 dollars for each douglas fir and N_02 dollars for each ponderosa pine. If the company paid N_03 ,500 dollars for the trees, how many firs and pines did they buy? | N_01 * v0 + N_02 * v1 = 217500.0 <BRG> v0 + v1 = N_00 | 100.0 750.0 | 850.0 300.0 250.0 217.0 |
Kevin bought N_00 muffins and a bottle of juice that cost N_01 dollars. He paid a total of N_02 dollars. How much did each muffin cost? | N_00 * v0 = N_02 - N_01 | 0.75 | 3.0 1.45 3.7 |
Norbert sold N_00 books on Thursday for a certain price. On Friday, he sold N_01 of the same books, but he charged N_02 dollars less per book. He made N_03 dollars in total. How much did the book sell for on Thursday? How much did the book sell for on Friday? | N_00 * v0 + N_01 * v1 = N_03 <BRG> v0 - v1 = N_02 | 8.75 8.25 | 23.0 35.0 0.5 490.0 |
A movie theater charges N_00 dollars for adults and N_01 dollars for children. The receipts for a showing of a movie were N_02 dollars. If N_03 tickets were sold, find how many adult tickets were sold. Find how many child tickets were sold. | N_00 * v0 + N_01 * v1 = N_02 <BRG> v0 + v1 = N_03 | 60.0 20.0 | 7.5 4.5 540.0 80.0 |
You have exactly N_00 dollars to spend on party gifts for your rich uncle's birthday party. You decide to get watches for the ladies at N_01 dollars each and beepers for the men at N_02 dollars each. You know that the number of watches required will be N_03 times as much as the number of beepers. How many watches do you buy? How many beepers do you buy? | N_02 * v0 + N_01 * v1 = N_00 <BRG> N_03 * v0 - v1 = 0.0 | 15.0 5.0 | 537.0 27.98 23.46 3.0 |
One out of two numbers is thrice the other. If their sum is N_00 , find the numbers. | v0 + v1 = N_00 <BRG> v1 - 3.0 * v0 = 0.0 | 31.0 93.0 | 124.0 |
Manuel opened a savings account with an initial deposit of N_00 dollars. If he wants to save N_01 dollars during the next N_02 weeks, how much must he save each week in dollars? | N_02 * v0 = N_01 - N_00 | 17.0 | 177.0 500.0 19.0 |
The number of grocery items on two grocery lists differs by N_00 . The total number of items is N_01 . How many items are on each list? | v0 + v1 = N_01 <BRG> v0 - v1 = N_00 | 13.0 20.0 | 7.0 33.0 |
The Drama Club sold N_00 tickets for the end-of-year-performance. Admission prices were N_01 dollars for adults and N_02 dollars for students. The total amount collected at the box office was N_03 dollars. How many students attended the play? How many adults attended the play? | N_01 * v0 + N_02 * v1 = N_00 <BRG> v0 + v1 = N_03 | 300.0 1200.0 | 1500.0 12.0 6.0 16200.0 |
If N_00 pesos can buy N_01 kilograms of fish and N_02 kilograms of pork while N_03 pesos can buy N_04 kilograms of fish and N_05 kilograms of pork, how much does a kilogram of fish cost? | N_01 * v0 + N_02 * v1 = N_00 <BRG> N_04 * v0 + N_05 * v1 = N_03 | 80.0 105.0 | 530.0 4.0 2.0 875.0 7.0 3.0 |
Arthur bought N_03 hamburgers and N_00 hot dogs for N_01 dollars. The next day, he bought N_02 hamburgers and N_03 hot dogs for N_04 dollars. How much does a hot dog cost? | N_03 * v0 + N_00 * v1 = N_01 <BRG> N_02 * v0 + N_03 * v1 = N_04 | 1.0 2.0 | 4.0 10.0 2.0 3.0 7.0 |
Old McDonald has N_00 goats and chickens on his farm. The animals combined have a total of N_01 legs. Assuming there are no physical defects, how many goats are on the farm? How many chickens are on the farm? | v0 + v1 = N_00 <BRG> 2.0 * v0 + 4.0 * v1 = N_01 | 2.0 13.0 | 15.0 34.0 |
The Rocket Coaster has N_00 cars, some that hold N_02 people and some that hold N_03 people. There is room for N_01 people altogether. How many N_02 -passenger cars are there? How many N_03 -passenger cars are there? | N_02 * v0 + N_03 * v1 = N_01 <BRG> v0 + v1 = N_00 | 9.0 6.0 | 15.0 72.0 4.0 6.0 |
A dealer has some hard candy worth N_02 dollars a pound and some worth N_03 dollars a pound. He wishes to make a mixture of N_00 pounds that he can sell for N_01 dollars a pound. How many pounds of N_02 -dollar candy does he need? How many pounds of N_03 -dollar candy does he need? | N_02 * v0 + N_03 * v1 = N_00 * N_01 <BRG> v0 + v1 = N_00 | 64.0 16.0 | 80.0 2.2 2.0 3.0 |
A theater has N_00 seats. On opening night, they sold out, selling adult tickets for N_01 dollars each and child tickets for N_02 dollars each. If they made a total of N_03 dollars, how many child tickets were sold? | N_01 * v0 + N_02 * v1 = N_03 <BRG> v0 + v1 = N_00 | 63.0 17.0 | 80.0 12.0 5.0 519.0 |
A catering company is setting up tables for a big event that will host N_00 people. When they set up the tables, they need N_01 forks for each child and N_02 forks for each adult. If the company ordered a total of N_03 forks, how many adults and how many children will be attending the event? | N_01 * v0 + N_02 * v1 = N_03 <BRG> v0 + v1 = N_00 | 488.0 276.0 | 764.0 2.0 5.0 2992.0 |
Jane has a dress shop. She has space for N_00 dresses. She sells only red and blue dresses. After reading several fashion magazines, she decides to stock her shelves with N_01 more blue dresses than red dresses. How many blue dresses and red dresses should she stock? | v0 + v1 = N_00 <BRG> v0 - v1 = N_01 | 117.0 83.0 | 200.0 34.0 |
A merchant wants to combine peanuts selling N_00 dollars per pound and cashews selling for N_01 dollars per pound to form N_02 pounds which will sell at N_03 dollars per pound. What amount of peanuts and what amount of cashews must be used? | N_00 * v0 + N_01 * v1 = N_02 * N_03 <BRG> v0 + v1 = N_02 | 50.0 10.0 | 2.4 6.0 60.0 3.0 |
Rowan can row N_00 kilometers downstream in N_01 hours. Returning upstream, it takes N_02 hours to complete the trip. Find his rate in still water in kilometers per hour and the rate of the current. | N_01 * v0 + N_01 * v1 = N_00 <BRG> N_02 * v0 - N_02 * v1 = N_00 | 9.75 3.25 | 26.0 2.0 4.0 |
For the first performance of a play in a community theater, N_00 reserved-seat tickets and N_01 general-admission tickets were sold. The total receipts were N_02 dollars. For the second performance, N_03 reserved-seat tickets and N_04 general-admission tickets were sold. The total receipts were N_05 dollars. Find the price of a reserved-set ticket in dollars. Find the price of a general-admission ticket. | N_00 * v0 + N_01 * v1 = N_02 <BRG> N_03 * v0 + N_04 * v1 = N_05 | 10.0 6.0 | 50.0 80.0 980.0 60.0 90.0 1140.0 |
One thousand quarts of milk testing N_00 butterfat are to be reduced to N_01 . How many quarts of cream testing N_02 butterfat must be separated from the milk to produce the required result? | N_01* v0 + N_02* v1 = 1000.0 * N_00 <BRG> v0 + v1 = 1000.0 | 50.0 950.0 | 0.04 0.03 0.23 |
Your teacher is giving a test worth N_00 points. There is a total of N_01 N_03 -point and N_02 -point questions. How many N_03 -point questions are on the test? | N_02 * v0 + N_03 * v1 = N_00 <BRG> v0 + v1 = N_01 | 20.0 10.0 | 200.0 30.0 10.0 5.0 |
Three times a number minus a second number is N_00 . The sum of the two numbers is N_01 . Find the two numbers. | 3.0 * v0 - v1 = N_00 <BRG> v0 + v1 = N_01 | 17.0 31.0 | 20.0 48.0 |
The sum of N_00 numbers is N_01 . Seven times the smaller number is the same as N_02 times the larger number. Find the smaller number. | 7.0 * v0 - N_02 * v1 = 0.0 <BRG> v0 + v1 = N_01 | 10.0 14.0 | 2.0 24.0 5.0 |
Seven times a number is the same as N_00 more than N_01 times the number. Find the number. | 7.0 * v0 - N_01 * v0 = N_00 | 3.0 | 12.0 3.0 |
The sum of N_00 of a number and two is eight. Find the number. | N_00 * v0 = 8.0 - 2.0 | 8.0 | 0.75 |
N_00 of a number decreased by N_01 is equal to N_02 . Find the number. | N_00 * v0 = N_01 + N_02 | 50.0 | 0.2 4.0 6.0 |
A store is selling compact discs for N_02 dollars and N_03 dollars. You buy N_00 discs and spend a total of N_01 dollars. How many compact discs did you buy that cost N_02 dollars? How many did you buy that cost N_03 dollars? | N_02 * v0 + N_03 * v1 = N_01 <BRG> v0 + v1 = N_00 | 4.0 6.0 | 10.0 93.0 10.5 8.5 |
A N_00 ounce can of cranberry juice sells for N_01 cents. Give the unit cost in cents per ounce. | N_00 * v0 = N_01 | 7.0 | 12.0 84.0 |
The sum of N_00 numbers is N_01 . N_02 of the first number plus N_03 of the second number is N_04 . Find the smaller and the larger number. | N_03 * v0 + N_02 * v1 = N_04 <BRG> v0 + v1 = N_01 | 12.0 15.0 | 2.0 27.0 0.5 0.3333333 11.0 |
Phyllis invested N_00 dollars, a portion earning a simple interest rate of N_03 per year and the rest earning a rate of N_04 per year. After N_01 year, the total interest earned on these investments was N_02 dollars. How many dollars did she invest at N_03 ? At N_04 ? | N_04* v0 +N_03* v1 = N_02 <BRG> v1 + v0 = N_00 | 18000.0 21000.0 | 39000.0 1.0 1980.0 0.04 0.06 |
N_00 number is N_01 less than twice another number. The sum of the N_02 numbers is N_03 . What is the smaller number? What is the larger number? | N_02 * v0 - v1 = N_01 <BRG> v0 + v1 = N_03 | 18.0 33.0 | 1.0 3.0 2.0 51.0 |
There are N_00 animals in a barn. Some are chickens, and some are pigs. There are N_01 legs in the barn. How many are pigs are there, and how many chickens are there? | v0 + v1 = N_00 <BRG> 2.0 * v0 + 4.0 * v1 = N_01 | 7.0 6.0 | 13.0 40.0 |
The admission fee at a small fair is N_00 dollars for children and N_01 dollars for adults. On a certain day, N_02 people enter the fair, and N_03 dollars is collected. How many children and adults attended? | N_00 * v0 + N_01 * v1 = N_03 <BRG> v0 + v1 = N_02 | 1500.0 700.0 | 1.5 4.0 2200.0 5050.0 |
Marco has N_00 coins, all nickels and dimes. He has N_01 more dimes than nickels. How many nickels and how many dimes does he have? | v0 + v1 = N_00 <BRG> v0 - v1 = N_01 | 69.0 81.0 | 150.0 12.0 |
N_00 less than N_01 times a number equals N_02 . What is the number? | N_01 * v0 = N_00 + N_02 | 5.0 | 7.0 4.0 13.0 |
Steve has N_00 coins consisting of dimes and nickels. If the value of the coins is N_01 dollars, then how many dimes does he have? | 0.1 * v0 + 0.05 * v1 = N_01 <BRG> v0 + v1 = N_00 | 26.0 10.0 | 36.0 3.1 |
N_00 trains leave simultaneously, traveling on the same track in opposite directions at speeds of N_01 and N_02 miles per hour. How many hours will it take before they are N_03 miles apart? | N_01 * v0 + N_02 * v0 = N_03 | 2.5 | 2.0 50.0 64.0 285.0 |
A piece of rope N_00 meters long is cut into two pieces so that the longest piece is twice as long as the shorter piece. How long are the two pieces? | v0 + v1 = N_00 <BRG> v1 - 2.0 * v0 = 0.0 | 20.0 40.0 | 60.0 |
The second number is N_00 less than twice the first number. Their sum is N_01 . Find the second number. | 2.0 * v0 - v1 = N_00 <BRG> v0 + v1 = N_01 | 37.0 20.0 | 3.0 57.0 |
In N_00 week, a music store sold N_01 guitars for a total of N_02 dollars. Electric guitars sold for N_03 dollars each, and acoustic guitars sold for N_04 dollars each. How many electric guitars were sold? How many acoustic guitars were sold? | N_03 * v0 + N_04 * v1 = N_02 <BRG> v0 + v1 = N_01 | 4.0 5.0 | 1.0 9.0 3611.0 479.0 339.0 |
N_00 of a number is N_01 . What is the number? | N_00 * v0 = N_01 | -72.0288 | 0.833 -60.0 |
N_00 number is N_01 less than twice another, and their sum is N_02 . Find the two numbers. | 2.0 * v0 - v1 = N_01 <BRG> v0 + v1 = N_02 | 17.0 25.0 | 1.0 9.0 42.0 |
Postcard stamps are N_00 dollars each. Letter stamps cost N_01 dollars each. If you have N_02 stamps worth N_03 dollars, how many postcard stamps do you have? How many letter stamps? | N_00 * v0 + N_01 * v1 = N_03 <BRG> v0 + v1 = N_02 | 30.0 20.0 | 0.2 0.33 50.0 12.6 |
Trenton sells electronic supplies. Each week he earns N_00 dollars plus commission, equal to N_01 of his sales. This week his goal is to earn no less than N_02 dollars. Write and solve an inequality to find the amount of sales he must make to reach his goal. | 0.01 * 4.0 * v0 = N_02 - N_00 | 7750.0 | 190.0 0.04 500.0 |
A truck and trailer together weigh N_00 pounds. The trailer weighs N_01 pounds less than N_02 as much as the truck. Find the truck's weight. Find the trailer's weight. | N_02 * v0 - v1 = N_01 <BRG> v0 + v1 = N_00 | 4800.0 2200.0 | 7000 200.0 0.5 |
Hockey teams receive N_00 points for a win and N_01 point for a tie. The wild cats once won a championship with N_02 points. They won N_03 more games than they tied. How many wins and how many ties did the Wildcats have? | N_00 * v0 + N_01 * v1 = N_02 <BRG> v0 - v1 = N_03 | 23.0 14.0 | 2.0 1.0 60.0 9.0 |
A new parking lot has spaces for N_00 cars. The ratio of spaces for full-sized cars to compact cars is N_01 to N_02 . How many spaces are for full-sized cars? How many spaces are for compact cars? | N_01 * v0 - N_02 * v1 = 0.0 <BRG> v0 + v1 = N_00 | 330.0 120.0 | 450.0 11.0 4.0 |
Dave and Sandy fly from Philly to Chicago, and it takes N_00 hours to go West and N_01 hours to fly East. The trip is N_02 miles one way. If the wind speed is the same on each trip, find the speed of the wind and find the speed of the plane in the still air, in miles per hour. | N_01 * v0 + N_01 * v1 = N_02 <BRG> N_00 * v0 - N_00 * v1 = N_02 | 65.0 455.0 | 2.0 1.5 780.0 |
A total of N_00 tickets were sold for the school play. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold? | v0 + v1 = N_00 <BRG> v1 - 2.0 * v0 = 0.0 | 122.0 244.0 | 366.0 |
A farmhouse has N_00 animals. Some are goats, and some are ducks. Altogether there are N_01 legs. How many of each animal are there? | v0 + v1 = N_00 <BRG> 2.0 * v0 + 4.0 * v1 = N_01 | 9.0 6.0 | 15.0 48.0 |
A special tea blend is made from two varieties of herbal tea, one that costs N_00 dollars per kilogram and another that costs N_01 dollars per kilogram. How many kilograms of each type are needed to make N_02 kilograms of a blend worth N_03 dollars per kilogram? | N_01 * v0 + N_00 * v1 = N_02 * N_03 <BRG> v0 + v1 = N_02 | 5.0 15.0 | 4.0 2.0 20.0 2.5 |
Didi invested a total of N_00 dollars in two accounts paying N_01 and N_02 simple interest. If her total return at the end of the first year was N_03 dollars, how much did she invest in each account? | N_01 * v0 + 0.01 * N_02 * v1 = N_03 <BRG> v1 + v0 = N_00 | 8000.0 4000.0 | 12000.0 0.075 0.06 840.0 |
One gallon container is full of a N_00 alcohol solution. How much must be drained off and replaced by a N_01 alcohol solution to produce one gallon of N_02 alcohol solution? | N_00 * v0 + N_01 * v1 = 1.0 * N_02 <BRG> v0 + v1 = 1.0 | 0.4 0.6 | 0.75 0.5 0.65 |
Colombian coffee beans cost N_00 dollars per pound, while Peruvian coffee beans cost N_01 dollars per pound. We want to mix the beans together so as to produce a N_02 -pound bag, costing N_03 dollars per pound. How many pounds of Colombian beans and how many pounds of Peruvian beans should be used? | N_00 * v0 + N_01 * v1 = N_02 * N_03 <BRG> v0 + v1 = N_02 | 11.2 28.8 | 5.5 4.25 40.0 4.6 |
Jerome bought N_00 CDs. Some cost N_01 ea. and the rest cost N_02 each. How many CDs were bought at each price if he spent N_03 dollars? | N_01 * v0 + N_02 * v1 = N_03 <BRG> v0 + v1 = N_00 | 4.0 8.0 | 12.0 7.5 6.5 82.0 |
The carpenter saws a board that is N_00 feet long into two pieces. One piece is to be N_01 foot longer than twice the length of the shorter piece. Find the Length of each piece. | v0 - 2.0 * v1 = N_01 <BRG> v0 + v1 = N_00 | 7.0 15.0 | 22.0 1.0 |
Cashews sell for N_00 dollars a pound, and peanuts sell for N_01 dollars a pound. How many pounds of peanuts and cashews would you use to make N_02 pounds of a mixture that sells for N_03 dollars? | N_00 * v0 + N_01 * v1 = N_03 <BRG> v0 + v1 = N_02 | 14.0 11.0 | 5.0 2.0 25.0 92.0 |
Bob invested N_00 dollars, part at N_03 and part at N_01 . If the total interest at the end of the year is N_02 dollars, how much did he invest at N_03 ? | N_03* v0 + N_01* v1 = N_02 <BRG> v1 + v0 =N_00 | 7000.0 15000.0 | 22000.0 0.14 3360.0 0.18 |
Find the amount of N_00 percent acid solution and the amount of a N_01 percent acid solution that Pat should combine to prepare N_02 cubic-centimeters of N_03 percent solution. | N_00 * v0 + N_01 * v1 = N_02 * N_03 <BRG> v0 + v1 = N_02 | 12.5 37.5 | 6.0 14.0 50.0 12.0 |
N_00 automobiles start out from two points N_01 kilometers apart and travel toward each other. The automobile from the east travels at N_02 kilometers faster than the automobile from the west. If they meet after N_03 hours, what is the average speed of each automobile? | N_03 * v0 + N_03 * v1 = N_01 <BRG> v1 - v0 = N_02 | 55.0 65.0 | 2.0 600.0 10.0 5.0 |
How many milliliters of a N_00 HCL solution should be combined with a N_01 HCL solution in order to get N_02 milliliters of a N_03 HCL solution? | 10.0 * v0 + 60.0 * v1 = N_02 * 30.0 <BRG> v0 + v1 = N_02 | 30.0 20.0 | 0.1 0.6 50.0 0.3 |
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