Question: Mark constructs a cube of pure gold. The cube is 6 cm on each side. The density of gold is 19 grams per cubic centimeter. He buys the gold for $60 per gram. He sells it for 1.5 times its gold value. What was the profit?
Answer: The cube is 6 * 6 * 6 = 216 cubic cm. So it has a mass of 216 * 19 = 4104 grams. So it uses 60 * 4104 = $246240. That means he sells it for 246240 * 1.5 = $369360. So he has a profit of 369360 - 246240 = $123,120. The answer is 123120.
[Question]A farmer living in the countryside has a certain number of children. One day, they followed him to the farm, each one with a bag to collect harvested apples. At the end of the day, each bag was filled with 15 apples each. On their way back home, 2 of the children have eaten 4 apples each and another child sold 7 of his apples. If they had a total of 60 apples left by the time they got home, how many children does the farmer have?
[Answer]2 children sold 4 apples each which gives 2 * 4 = 8 apples. Another child gave out an additional 7 apples making 8 + 7 = 15 apples removed from the total. There were 60 apples left after these, so the original total must have been 15 + 60 = 75 apples. Each child collected 15 apples so there are 75 / 15 = 5 children. The answer is 5.
Q: Big Dig Mining Company mines three different types of ore: copper, iron, and nickel. Across all their mines, 10% of their output is nickel, 60% is iron, and the rest is copper. They mine 720 tons of nickel a day. How many tons of copper does Big Dig Mining Company mine daily?
A: Let R be the total ore output of the company. Of Big Dig’s output, 100 - 10 - 60 = 30% is nickel. Since 720 is 60% of 100% of their output, 720 / R = 60 / 100. Thus, Big Dig mines R = 100 * 720 / 60 = 1200 tons of ore daily. Therefore, Big Dig mines 1200 * 30 / 100 = 360 tons of copper daily. The answer is 360.
Question: James and John combine their friends lists. James has 75 friends. John has 3 times as many friends as James. They share 25 friends. How many people are on the combined list?
Answer: John has 75 * 3 = 225 people on his friends list. So that means there are 225 + 75 = 300 people on the list. So once you remove duplicates there are 300 - 25 = 275 people. The answer is 275.
[Question]On Sunday Alice bought 4 pints of strawberry ice cream. The next day she went back and bought three times that number of pints. On Tuesday she bought one-third of the number of pints she bought the day before. On Wednesday she returned half of the pints she bought the day before because they were expired. How many pints of ice cream did she have on Wednesday?
[Answer]On Monday she bought 4 * 3 = 12 pints. On Tuesday she bought 12 / 3 = 4 pints. Before she returned any she had 4 + 12 + 4 = 20 pints. She returned 4 / 2 = 2 pints. After returning she had 20 - 2 = 18 pints. The answer is 18.
[Question]Dexter and Jay are using a gallon of white paint to paint the walls. Dexter used 3/8 of the gallon of paint while Jay used 5/8 of a gallon of paint. If a gallon is equal to 4 liters, how many liters of paint were left from Dexter and Jay combined?
[Answer]
Dexter used 4 x 3 / 8 = 3 / 2 liters of paint. Jay used 4 x 5 / 8 = 5 / 2 liters of paint. Together, they used 3 / 2 + 5 / 2 = 4 liters of paint. Since each of them used a gallon of paint, then they both used 2 x 4 = 8 liters of paint together. Therefore, 8 - 4 = 4 liters of paint were left. The answer is 4.