Lower Elementary:
Question: Courtney has 72 grapes. She ate half of them for lunch. She ate half of what left after lunch for a late night snack. How many grapes are left?
Answer: 18 grapes
Solution: First, let’s find out how many grapes are left after lunch. Half of 72 = half of 70 + half of 2 = 35 + 1 = 36. There are 36 grapes left after lunch. Now, let’s find out how many grapes there are after the late night snack. Half of 36 = half of 30 + half of 6 = 15 + 3 = 18. There are 18 grapes left.
Upper Elementary:
Question: Frank is saving for a video game console that costs $100 and a video game that costs $50. He already has $30 saved. He earns $15 for every lawn that he mows. How many lawns must he mow in order to buy both the console and the game?
Answer: 8 lawns
Solution: The video game console costs $100 and the video game costs $50. That means he needs a total of $100 + $50 = $150. He already has $30 saved, so he needs $150 – $30 = $120 more dollars. He earns $15 for each lawn that he mows. So, he needs to mow 120 ÷ 15 = 8 lawns to have enough money.
Middle School:
Question: A dance team’s set contains three songs. The first song is 2/5 of the whole set length. The second song is 25% of the set whole length. The third song is 1 minute and 45 seconds long. How long is the whole set?
Answer: 5 minutes, or 300 seconds
Solution: To solve this problem we need to find the part of the set length that the third song represents because we know how long the third song is. We can then find the whole set length. To find a fractional part, we take the whole and subtract the sum of the other parts. 25% is the same as ¼, so the first and second songs together are 2/5 + 1/4 = 8/20 + 5/20 = 13/20 of the whole set. 1 – 13/20 = 7/20. So, the third song is 7/20 of the set length. 1 minute and 45 seconds is the same as 105 seconds. If we break 105 seconds into 7 equal parts, each part is 15 seconds. So, 1/20 of the set length is 15 seconds. That means the entire length is 15 seconds × 20 = 300 seconds, or 5 minutes.
Algebra and Up:
Question: Solve for x: 92x–3 = 273x –7
Answer: 3
Solution: One way to solve this problem is to have the same number as the base and then set the exponents equal to one another. Since 9 = 32 and 27 = 33, we can rewrite our problem as the following:
32(2x – 3) = 33(3x – 7)
Now that the bases are the same, we can set the exponents equal to each other and solve for x.
2(2x – 3) = 3(3x – 7)
Distribute.
4x – 6 = 9x – 21
Subtract 4x from both sides and add 21 to both sides.
15 = 5x
Divide both sides by 5.
3 = x
So, x = 3.
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