Lower Elementary:
Question: Angie is watching an ant colony for a few weeks. In the first week, she saw 27 ants. In the second week, there were twice as many as there were in the first week. In the third week, there were twice as many as there were in the second week. How many ants does Angie see in the third week?
Answer: 108 ants
Solution: First, we need to find the number of ants that there were in the second week. To find the number of ants in the second week, double the number of ants that there were in the first week. To double 27, break it into two parts, double each part, and then add them together.
27 doubled = 20 doubled + 7 doubled = 40 + 14 = 54.
There are 54 ants on the second week. To find the number of ants in the third week, double the amount of ants that there were in the second week.
54 doubled = 50 doubled + 4 doubled = 100 + 8 = 108
There are 108 ants on the third week.
Upper Elementary:
Question: Drew planted 5 orange trees. Each tree grew 10 oranges. Drew then sold all of the oranges for $2.50 each. How money did Drew make selling all of the oranges.
Answer: $125
Solution: First, we need to find the total number of oranges Drew had to sell. To find the total, multiply the number of trees by the number of oranges on each tree. 5 × 10 = 50. Drew had 50 oranges. To find out how much Drew made selling oranges, multiply the total number of oranges by the amount he sells each orange for. 50 × 2.50 = $125.00. Drew made $125 selling all of the oranges.
Middle School:
Question: Sixty plus five times a number is three times the same number. What is the number?
Answer: –30
Solution: Let n be the number that we are trying to solve for. Translating the verbal statement into an algebraic equation, we have
60 + 5n = 3n
One way to solve this problem is to subtract 5n from both sides of the equation.
60 = –2n
Divide both sides of the equation by –2.
–30 = n
The number is –30.
Algebra and Up:
Question: In order to win a particular game, you have to flip 2 fair quarters, get heads on both, and then roll a 4 on a fair die. What is the probability of winning the game?
Answer: 1/24 or 4.16%
Solution: To find the probability of winning the game, multiply the probabilities of getting each of the conditions. The probability of flipping a head on a fair coin is 1/2. So to flip 2 heads in a row, it is 1/2 × 1/2 = 1/4. The probability of rolling a 4 on a fair die is 1/6. 1/4 × 1/6 = 1/24. There is a 1/24, or 4.16%, probability of winning the game.
