Lower Elementary:
Question: The temperature on Monday was 20 degrees cooler than it was on Wednesday. The temperature Wednesday was 15 degrees hotter than it was on Friday. If it was 80°F on Friday, what was the temperature on Monday?
Answer: 75°F
Solution: Let’s start by finding the temperature on Wednesday. It was 15 degrees hotter on Wednesday than on Friday so add 15 degrees to Friday’s temperature to get Wednesday’s temperature. 80 + 15 = 95. It was 95°F on Wednesday. It was 20 degrees cooler on Monday, so subtract 20° from Wednesday’s temperature to get Monday’s temperature. 95 – 20 = 75. It was 75°F on Monday.
Upper Elementary:
Question: Gary is putting away 120 blocks into 6 boxes: 1 large and 5 small. Half of the blocks go into the large box. An equal amount of blocks are put into each of the 5 small boxes. How many blocks are put into one small box?
Answer: 12 blocks
Solution: Half of 120 is 60. That means that 60 blocks are put in the large box and there are 60 left over to put in the small boxes. Divide 60 by 5 to see how many blocks are put in each small box. 60 ÷ 5 = 12. Each small box contains 12 blocks.
Middle School:
Question: Alexis runs at an average speed of 6 feet per second. How many minutes will it take for her to run a trail that is 1,200 yards long?
Answer: 10 minutes
Solution: To find how long it will take, we need the units to have the same name: her speed is in feet per second and the distance is in yards. One way is to convert the yards to feet by multiplying by 3 because there are 3 feet in 1 yard. 1,200 × 3 = 3,600. So now we calculate how long it would take her to run 3,600 feet. To see how long it takes, divide the distance traveled by the rate at which Alexis runs. 3,600 ÷ 6 = 600 seconds. It takes Alexis 600 seconds to run the trail. To convert seconds to minutes, divide by 60 because there are 60 seconds in 1 minute. 600 ÷ 60 = 10. It would take Alexis 10 minutes to run the trail.
Algebra and Up:
Question: Let k be 10% of a number. What is 60% of the number? (leave your answer in terms of k)
Answer: 6k
Solution: Let n be the number. To find 10% of the number we can multiply by 0.1, which is 10% written as a decimal. We can write the value of k as k = 0.1n. Now we want to know what 60%, or 0.6, of the number is. To do that we multiply both sides by 6 because 0.1 × 6 = 0.6 = 60%. 6k = 0.6n. So, 60% of the number is 6k.
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