Lower Elementary:
Question: Markus has a $50 gift card for a restaurant. On one visit, he spent $20 of his gift card. On the next visit, the bill was $45. Markus used the remaining money on the gift card and then paid the rest with cash. How much cash did Markus need to pay the bill?
Answer: $15
Solution: On his first visit, he spent $20, so now Markus has $30 left on his gift card (50 – 20 = 30). The second visit’s bill total was $45. He used the $30 left on his card, so the difference is how much cash Markus would have to pay. 45 – 30 = 15. Markus paid $15 in cash to pay the bill.
Upper Elementary:
Question: A water polo game has 4 quarters, and each quarter is 7 minutes. If it is half way through the third quarter, how many minutes are left in the game?
Answer: 10 1/2 minutes
Solution: One way to solve this is to calculate how many quarters of the game are left and then find how long that would be. If we are half way through the third quarter, then there is half of the third quarter and the whole fourth quarter left. A whole quarter is 7 minutes, so half of a quarter is 3 ½ minutes. Time for half of the third quarter + time for the whole fourth quarter = 3 ½ + 7 = 10 ½. There are 10 ½ minutes left in the game.
Middle School:
Question: What is the sum of all odd numbers from 1 to 49?
Answer: 625
Solution: If we write out the numbers in a line, we have 1 + 3 + 5 + 7 + 9 + 11 + … + 39 + 41 + 43 + 45 + 47 + 49. Notice that if we add the 1 and 49, we get 50. If we add 3 and 47, we get 50. This pattern continues throughout, and then stops when we get to 25. So there are 12 pairs of 50 and the 25. 50, 12 times is 600 and then adding the 25, the total sum is 625.
Algebra and Up:
Question: A number squared plus six times the quantity of the number plus two is eight less than negative three times the same number. Two numbers make this statement true. What are the numbers?
Answer: –4 and –5
Solution: Let x be the number. Writing the statement as a math equation, we have:
x2 + 6(x + 2) = –3x – 8
Distribute the 6.
x2 + 6x + 12 = –3x – 8
Add 3x + 8 to both sides of the equation.
x2 + 9x + 20 = 0
Factor the equation.
(x + 4)(x + 5) = 0
Set each quantity equal to 0 to find the number.
x + 4 = 0
x = –4
x + 5 = 0
x = –5
The two numbers are –4 and –5
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