Lower Elementary
Question: Caitlin and Isabela both started out with $56 each. Caitlin bought a shirt for $17 and Isabela’s mother gave her $23. How much more money does Isabela have than Caitlin now?
Answer: $40
Note: To find out how much more money Isabela has then Caitlin, first subtract the money Caitlin spent from her original amount. 56 – 17 = 39. Caitlin now has $39. Then add $23 to Isabela’s original amount. 56 + 23 = 79. Isabela now has $79. Then subtract Caitlin’s money from Isabela’s. 79 – 39 – 40. Isabela has $40 more than Caitlin.
Upper Elementary
Question: Mr. Smith’s gym class ran around a rectangular track. The track is 86 yards by 33 yards. The class ran around the track four times. How far did the class run?
Answer: 952 yards
Note: To find the distance the class ran, first find the perimeter of the track. If the track is 86 yards by 33 yards then the total distance around is 86 + 86 + 33 + 33 = 238 yards. Since they ran around four times, to find the total distance they ran multiply 238 by 4. 238 x 4 = 952. The class ran 952 yards.
Middle School
Question: Sarah took a metal wire that is 96 inches long and bent it into a rectangle. The width was 11 1/4 inches. What was the length?
Answer: 36 3/4 inches
Note: Since the wire is 96 inches long when Sarah bent it into the shape of a rectangle, the perimeter of the rectangle is 96 inches. Since the width is 11 1/4 inches, to find the length multiply the width by 2 (11 1/4 x 2 = 22 1/2). Then subtract from the perimeter 96 – 22 1/2 = 73 1/2. This value is two times the length of the rectangle. To find the length divide 73 1/2 by 2 which gives 36 3/4. The length of the rectangle is 36 3/4 inches.
Algebra and Up
Question: Working together, Joshua and Daniel can complete a job in 2 hours. Working alone, Daniel can do the job in 5 hour. How long would it take Joshua to do the job by himself?
Answer: 10/3 hours or 3 hours 20 minutes or 200 minutes
Note: This is a “work” problem. The formula for solving a work problem is in the following:
T/time for person 1 + T/time for person 2 = 1
For this problem:
T = 2 hours
time for person 1 (Daniel) = 5 hours
time for person 2 (Joshua) = x
Next, set up the equation and solve for Joshua’s time.
2/5 + 2/x = 1
Multiply the equation through by the least common multiple of the denominators: 5x
2x + 10 = 5x
10 = 3x
10/3 = x
It takes Joshua 10/3 hours. This can also be expressed as 3 hours 20 minutes or 200 minutes.