Question: A school cafeteria uses ground mince to cook lasagnas and cottage pies. They make 100 lasagnas, which use 2 pounds of ground mince each, and cottage pies, which use 3 pounds of ground mince each. If the cafeteria has used 500 pounds of ground mince in total, how many cottage pies did they make?
Answer: The cafeteria used 100 lasagnas * 2 pounds of ground mince = 200 pounds of ground mince for the lasagnas. This means they used 500 pounds of ground mince in total – 200 pounds of ground mince for the lasagnas = 300 pounds of ground mince for the cottage pies. So they must have made 300 pounds of ground mince for the cottage pies / 3 pounds of ground mince per cottage pie = 100 cottage pies. The answer is 100.

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: We harvested 405 kg of apples. 90 kg were used to make fruit juice and 60 kg were given to a restaurant. The rest was sold in 5 kg bags and their sale brought in $408. What was the selling price of one bag of apples?
Answer: The weight of apples used for juice and given to the restaurant is 60 + 90 = 150 kg. Thus 405 – 150 = 255kg worth of apples were sold in 5 kg bags. There were 255 / 5 = 51 bags sold. So each bag was sold for 408 / 51 = $8. The answer is 8.

Question: April went to a concert that has two bands. 2/3 of the audience was there for the second band and 1/3 was there for the first band. 50% of the audience there for the second band is under the age of 30. Of this group, 60% are women and there are 20 men. How many people are at the concert?
Answer:
Of the under - 30s there for the second band, 40% are men because 100 - 60 = 40. There are fifty under - 30s there for the second band because 20 / .4 = 50. There are 100 people there to see the second band because 50 / .5 = 100. There are 150 people at the concert because 100 / (2 / 3) = 150. The answer is 150.