Q: Derrick measures the length of his yard. The length of Alex's yard is half the size of Derrick's and the length of Brianne's yard is 6 times the size of Alex's. If Brianne's yard is 30 yards long, how long is Derrick's yard, in yards?
A: The length of Alex's yard is 30 / 6 = 5 yards. The length of Derrick's yard is 5 * 2 = 10 yards. The answer is 10.
Question: Carl is figuring out how much he'll need to spend on gas for his upcoming road trip to the Grand Canyon. His car gets 30 miles per gallon in cities and 40 miles per gallon on the highway. The distance from his house to the Grand Canyon, one way, is 60 city miles and 200 highway miles. If gas costs $3.00 per gallon, how much will Carl need to spend?
Answer: First figure out how many city miles Carl will drive round trip by multiplying the one - way number of city miles by 2: 60 miles * 2 = 120 miles. Then figure out how many highway miles Carl will drive round trip by multiplying the one - way number of highway miles by 2: 200 miles * 2 = 400 miles. Now divide the round - trip number of city miles by the number of city miles per gallon Carl's car gets: 120 miles / 30 mpg = 4 gallons. Now divide the round - trip number of highway miles by the number of highway miles per gallon Carl's car gets: 400 miles / 40 mpg = 10 gallons. Now add the gallons for the highway miles and the city miles to find the total number of gallons Carl needs to buy: 10 gallons + 4 gallons = 14 gallons. Finally, multiply the number of gallons Carl needs to buy by the cost per gallon to find out how much he spends: 14 gallons * $3.00 = $42.00. The answer is 42.
[Question]Jenna runs a wholesale business. She pays $3 for each widget and resells it for $8. Every month she has to pay $10,000 in rent, 20% of her total profit in taxes, and $2,500 each to four workers. If Jenna sells 5000 widgets one month, how much is her total profit or loss?
[Answer]First calculate how much Jenna spends on salaries: $2,500 * 4 = $10,000. Next find Jenna's total fixed costs by adding the cost of salaries and rent: $10,000 + $10,000 = $20,000. Next calculate how much profit Jenna makes on each widget by subtracting the cost from the sale price: $8 - $3 = $5. Now multiply the profit per widget by the number of widgets sold: $5 * 5000 = $25,000. Now subtract Jenna's costs from her sales to find her total profit before taxes: $25,000 - $20,000 = $5,000. Now multiply Jenna's profit by her 20% tax rate to find how much she owe in taxes: $5,000 * .2 = $1,000. Now subtract Jenna's taxes from her profit before taxes to find her total profit: $5,000 - $1,000 = $4,000. The answer is 4000.
Q: Martha gets prize points every time she shops at her local grocery store. She gets 50 points per $10 spent, plus a 250 point bonus if she spends more than $100. Martha buys 3 pounds of beef for $11 each, 8 pounds of fruits and vegetables for $4/pound, 3 jars of spices for $6 each, and other groceries totaling $37. How many points does Martha get?
A: First find the total cost of the beef: $11 / pound * 3 pounds = $33. Then find the total cost of the fruits and vegetables: $4 / pound * 8 pounds = $32. Then find the total cost of the spices: $6 / jar * 3 jars = $18. Now add the cost of all the items to find Martha's total spending: $33 + $32 + $18 + $37 = $120. Now divide 50 points by $10 to find now many points Martha gets per dollar: 50 points / $10 = 5 points / dollar. Now multiply this exchange rate by Martha's total spending to find how many points she gets before the bonus: $120 * 5 points / dollar = 600 points. Finally, add the 250 point bonus Martha gets for spending more than $100: 600 points + 250 points = 850 points. The answer is 850.
Question: A radio show plays for 3 hours a day. They split their show into talking segments, ad breaks and songs. Talking segments last 10 minutes each, ad breaks last 5 minutes each and songs are played throughout the rest of the show. If the radio show includes 3 talking segments and 5 ad breaks in today's show, how long, in minutes, does the show play songs?
Answer: The entire radio show plays for 3 hours * 60 minutes = 180 minutes. The talking segments use 3 talking segments * 10 minutes per talking segment = 30 minutes each. The ad breaks use 5 ad breaks * 5 minutes per ad break = 25 minutes. In total, the talking segments and ad breaks use 30 + 25 = 55 minutes. This leaves 180 55 = 125 minutes for the radio show to play songs. The answer is 125.
Q: The moon is made of 50% iron, 20% carbon, and the remainder is other elements. Mars weighs twice as much as the moon, but has the exact same composition. If Mars is 150 tons of other elements, how many tons does the moon weigh?
A:
30% of Mars is made up of other elements because 100 - 50 - 20 = 30. Mars weighs 500 tons because 150 / .3 = 500. The moon weighs 250 tons because 500 / 2 = 250. The answer is 250.