Lower Elementary:
Question: Jane has 72 seashells. She used half of the seashells to make a necklace. She used half of what was left to decorate a shadow box. How many seashells does Jane have left?
Answer: 18 seashells
Solution: Jane used half of her 72 seashells to make a necklace. Half of 72 is 36 (half of 72 = half of 70 + half of 2 = 35 + 1 = 36). Jane has 36 seashells left after making the necklace. She then used half of what was left to decorate a shadow box. Half of 36 is 18 (half of 36 = half of 30 + half of 6 = 15 + 3 = 18). Jane has 18 seashells left.
Upper Elementary:
Question: At a fabric store, blue fabric is sold for $10.50 a yard and red fabric is sold for $9 a yard. How much would 4 ½ yards of blue fabric and 3 ½ yards of red fabric cost altogether?
Answer: $78.75
Solution: First, let’s find the cost of the blue fabric. The cost of 4 yards of blue fabric is $42 (10.50 × 4 = 42). Half a yard of blue fabric costs $5.25, so the cost of 4 ½ yards of blue fabric is $47.25 (42 + 5.25 = 47.25). Now let’s find the cost of the red fabric. The cost of 3 yards of red fabric is $27 (9 × 3 = 27). Half a yard of red fabric costs $4.50, so the cost of 3 ½ yards of red fabric is $31.50 (27 + 4.50 = 31.50). The total cost of 4 ½ yards of blue fabric and 3 ½ yards of red fabric is $78.75 (47.25 + 31.50 = 78.75)
Middle School:
Question: Dan can run 1.5 miles in 10 minutes. How fast is this in feet per hour?
Answer: 47,520 feet per hour
Solution: One way to solve this problem is to convert the minutes into hours first, then convert the mile to feet. There are 60 minutes in an hour and 6 × 10 minutes = 60 minutes. If Dan can run 1.5 miles in 10 minutes, then he can run 9 miles in an hour (1.5 × 6 = 9). There is 5,280 feet in one mile. 5,280 × 9 = 47,520. Dan’s running rate is 47,520 feet per hour.
Algebra and Up:
Question: Henry can make a stuffed animal in 6 hours. Nina can make a stuffed animal in 4 hours. If Henry and Nina work together, how long will it take for them to make one stuffed animal?
Answer: 2 hours and 24 minutes
Solution: One way to solve the problem is to find how much of the stuffed animal that Henry and Nina can make separately in one hour and then add them together. Let t be the time it takes for them to make one stuffed animal together. Henry can make 1/6 of the stuffed animal in an hour and Nina can make 1/4 of the stuffed animal in an hour.
1/6 + 1/4 = 1/t
Multiply both sides by 12t to cancel out the denominators.
2t + 3t = 12
Combine like terms.
5t = 12
Divide by 5.
t = 12/5 = 2 2/5 = 2 hours and 24 minutes
Working together, it takes Henry and Nina 2 hours and 24 minutes to make one stuffed animal.
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