Q: Michael and Thomas are selling their lego collections. They agree to split any money they earn. They sell them based on how many circles are on top. Each circle costs 1 cent. They earned $5 each after selling 100 single pieces, 45 double pieces, 50 triple pieces and a number of quadruple pieces. How many quadruple pieces did they sell?
A: They made $10 because 2 x 5 = 10. They made $1 off single pieces because 100 x .01 = 1. They made $.9 off double pieces because 45 x .02 = .9. They made $1.5 off triple pieces because 50 x .03 = 1.5. They earned $3.4 off the first three types because 1 + .9 + 1.5 = 3.4. They earned $6.6 off the quadruple pieces because 10 - 3.4 = 6.6. They sold 165 quadruple pieces because 6.6 / .04 = 165. The answer is 165.
Question: There are several cookies in the jar. Taking 1 cookie away would leave half as many in the jar as if 5 were added. How many cookies are in the jar?
Answer: Let C be the number of cookies. There would be C - 1 cookies. There would be (C + 5) / 2 cookies. C - 1 = (C + 5) / 2. 2(C - 1) = C + 5. 2C - 2 = C + 5. C = 7. The answer is 7.
[Question]Michael is baking a cake and needs 6 cups of flour. The only measuring cup he has is the 1/4 cup. He has an 8 cup bag of flour and realizes it would be faster to measure the flour he doesn't need, take it out of the bag, and then dump the rest of the bag into the bowl. How many scoops should he remove?
[Answer]He needs to remove 2 cups of flour because 8 minus 6 equals 2. He needs to use 8 scoops because 2 divided by .25 equals 8. The answer is 8.
Q: An apartment complex has 4 identical buildings. Each building has 10 studio apartments, 20 2 person apartments, and 5 4 person apartments. How many people live in the apartment complex if it has 75% of its maximum occupancy?
A: First, we find out how many people live in each building. In addition to 10 1 person apartments, as a studio apartment is for a single person, there are 20 2 person apartments meaning there are 20 * 2 = 40 people capable of living there. We then find out how many people can live in the 4 person apartments by multiplying the number of available 4 person apartments by 4, performing 5 * 4 = 20 people capable of living there. So, in 1 building there is room for 10 + 40 + 20 = 70 people. We multiply this by the 4 buildings in total, finding a maximum occupancy of 4 * 70 = 280 people. We then multiply this by .75 to find out how many people would live there at 75% of maximum occupancy, performing 280 * .75 = 210 people. The answer is 210.
Question: Ronald is rolling a die and won't stop rolling until the average of all his rolls is a 3. He rolls a 1, a 3, a 2, a 4, a 3, a 5, a 3, a 4, a 4 and a 2. What does he need to roll on the next roll to be able to stop?
Answer: The next roll will be his 11th roll. The total on this tenth roll to have an average of 3 is 33, because 3 * 11 = 33. His current total is 31 because 1 + 3 + 2 + 4 + 3 + 5 + 6 + 1 + 4 + 2 = 31. He needs to roll a 2 because 33 - 31 = 2. The answer is 2.
Q: Mark and his sister Chris both leave their house for school at the same time. Mark travels at the same speed as Chris, who walks 3 miles per hour. After walking 3 miles Mark has to turn around and go home because he forgot his lunch. If the distance from their house to the school is 9 miles, how much longer does Mark spend walking than Chris?
A:
First find the total number of miles Mark walks to get his lunch by multiplying the distance he walks back to the house by 2: 3 miles * 2 = 6 miles. Then find the total distance Mark walks by adding that distance to the distance between the house and the school: 6 miles + 9 miles = 15 miles. Now divide the total distance Mark walks by his speed to find how many hours he spends walking: 15 miles / 3 miles / hour = 5 hours. Now divide the total distance Chris walks by her speed to find the total time she spends walking: 9 miles / 3 miles / hour = 3 hours. Now subtract the time Chris spends walking from the time Mark spends walking to find the difference: 5 hours - 3 hours = 2. The answer is 2.