Lower Elementary:
Question: Yosephine baked 30 cookies. She gave 18 of the cookies to her friends. When Yosephine’s grandmother visited, she gave Yosephine 25 more cookies. How many cookies does Yosephine have now?
Answer: 37 cookies
Solution: Yosephine started with 30 cookies. She gave 18 cookies to her friends, so now she has 12 cookies left (30 – 18 = 12). Yosephine’s grandmother gave her 25 cookies. Now Yosephine has 37 cookies (12 + 25 = 37).
Upper Elementary:
Question: On Monday, Tommy ordered one whole pizza and ate half of it for dinner. On Tuesday, he ate half of what was left for lunch and ate half what was left after lunch for dinner. How much of the pizza did Tommy eat altogether?
Answer: 7/8 of the pizza
Solution: Tommy started with one whole pizza. He ate half for dinner, so now there is half (1/2) of a pizza left. He ate half of what was left for lunch on Tuesday. Half of a half is a quarter (1/4), so he ate a quarter of the pizza and there is a quarter left. He ate half of what was left for dinner on Tuesday. Half of a quarter is an eighth (1/8), so there is an eighth of the pizza left. If there is an eighth of the pizza left, then Tommy ate 7/8 of the pizza (1 whole – 1/8 = 7/8).
Middle School:
Question: A music store is having a sale with a 15% discount on the price of pianos. If a piano originally costs $1,000 and Hank pays for the discounted price with $900, how much change will he get back?
Answer: $50
Solution: First we need to find the discounted amount of the piano. Percent means “for each hundred.” There are 10 hundreds in 1,000 so we count 15, 10 times to get the amount of the discount. 15 × 10 = 150. The piano’s discounted price is $150 less than the original price. This means that the discounted price of the piano is $850. If Hank pays $900, then he will get $50 back in change ($900 – $850 = $50).
Algebra and Up:
Question: Five less than two times an integer squared equals the same integer plus ten. What is the integer?
Answer: 3
Solution: Let x be the integer. Writing the statement as an algebraic equation, we have:
2x2 – 5 = x + 10
One way to solve this equation is to move everything to one side of the equation.
2x2 – x – 15 = 0
Factor the equation.
(2x + 5)(x –3) = 0
Our solutions to the algebraic equation are –5/2 and 3. Since the question said that the number was an integer, our answer is 3.
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