Lower Elementary:
Question: Emma has 36 eggs. She used half of them to make omelets for her family. She then used half of what was remaining for baking. How many eggs does Emma have left?
Answer: 9 eggs
Solution: Emma used half of the eggs to make omelets. Half of 36 = half of 30 + half of 6 = 15 + 3 = 18. She has 18 eggs left after making the omelets. She used half of what was remaining for baking. Half of 18 = half of 10 + half of 8 = 5 + 4 = 9. She has 9 eggs left.
Upper Elementary:
Question: Hamburger patties are sold in packs of 12 patties. Hamburger buns are sold in packs of 8. What is the fewest amount to buy of each so that there are no leftovers of either patties or burgers and so that there is enough to make at least 30 hamburgers?
Answer: 4 packs of patties and 6 packs of buns
Solution: We have to find a common multiple of 8 and 12. Multiples of 8 are 8, 16, 24, 32, 40, and 48. Multiples of 12 are 12, 24, 36, 48, and 60. The least common multiple of 8 and 12 is 24. However, we need to make at least 30 hamburgers, so we need to find the next common multiple, which is 48. Since 48 is more than 30, we need 4 packs of patties (12 × 4 = 48) and 6 packs of buns (8 × 6 = 48).
Middle School:
Question: Yumi’s average on her 4 tests is 80. If she scores a 90 on her fifth test, what is her new test average?
Answer: 82
Solution: The average of her first 4 test scores is 80. That means the total score of her first 4 tests is 320 (80 × 4 = 320). If she scored 90 on her fifth test, then her new test total is 410 (320 + 90 = 410). Since she took 5 tests, to find the average we divide by 5. 410 ÷ 5 = 82. Her new test average is 82.
Algebra and Up:
Question: The sum of three consecutive even integers is 252. What are the three numbers?
Answer: 82, 84, and 86
Solution: Let n be the smallest of the three numbers. To get the next even integer, we add 2. So the second number is n + 2. The next even integer is 2 more than the previous number. So, 2 + n + 2 = n +4. We know that these three numbers add to 252, so we have:
n + (n + 2) + (n + 4) = 252
Combine the like terms.
3n + 6 = 252
Subtract 6 from both sides.
3n = 246
Divide by 3.
n = 82
The first even integer is 82. This means that the next numbers are 84 and 86.
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