Math Problem Monday - Jan 15th, 2018 | Mathnasium Livermore, CA

Jan 15, 2018 | Livermore

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.

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