Lower Elementary:
Question: Jack did 12 push-ups on Monday. On Wednesday, he did twice as many push-ups as he did on Monday. On Friday he did twice as many push-ups as he did on Wednesday. How many push-ups did Jack do on Friday?
Answer: 48 push-ups
Solution: First, we need to find how many push-ups Jack did on Wednesday. He did twice as many push-ups on Wednesday as he did on Monday. He did 12 push-ups on Monday. 12 doubled = 10 doubled + 2 doubled = 20 + 4 = 24. He did 24 push-ups on Wednesday. He did twice as many push-ups on Friday as he did on Wednesday. 24 doubled = 20 doubled + 4 doubled = 40 + 8 = 48. Jack did 48 push-ups on Friday.
Upper Elementary:
Question: Jeanie has a collection of pens. A fourth of the pens are black, a fifth of the pens are red, a tenth of the pens are green, and the remaining 18 pens are blue. How many pens does Jeanie have altogether?
Answer: 40 pens
Solution: One way to solve this problem is to find the fractional part of the pens that are blue. To find the part that is blue, subtract the sum of the other parts from the whole. Let’s add the other parts first. In order to add the fractions, they must have the same denominator, or the same name. 1/4 + 1/5 + 1/10 = 5/20 + 4/20 + 2/20 = 11/20. Now we subtract from 1 whole. 1 – 11/20 = 9/20. This means that 18 pens represent 9/20 of the pen collection. By breaking 18 into 9 equal parts, we know that 2 pens represents 1/20 of the collection. That means that the entire collection contains 40 pens.
Middle School:
Question: Zack uses a coupon to buy a video game console for 15% off. He also has a $20 gift card, so that he only has to pay $134.70 for video game console. What was the original price of the video game console?
Answer: $182
Solution: First we have to find what the reduced cost of the video game console was. Zack paid $134.70 and used a $20 gift card, so the reduced cost of the console after the discount is $154.70. Since the console is 15% off, that means the reduced cost is 85% of the original price of the video game console. 85% of the original cost will give the reduced cost of $154.70. One way to solve this is to divide $154.70 by the 85%. 154.70 ÷ 0.85 = 15,470 ÷ 85 = 182. The original cost of the video game console is $182.
Algebra and Up:
Question: Find the probability of drawing an ace or a clubs from a standard deck of cards.
Answer: 16/52 = 4/13
Solution: There are 52 cards in a standard deck of cards. Each suit has 13 cards in it, so there are 13 clubss in the deck. There are 4 copies of each denomination: one for each suit. So there are 4 aces in the deck. However, the ace of clubss satisfies both conditions and we counted it twice. So, the number of cards in the deck that are clubss or aces is 13 + 4 – 1 = 16. The probability of drawing an ace or a clubs from a standard deck of cards is 16/52 = 4/13.
