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### Math Problem Monday - Oct 23rd, 2017 | Mathnasium Livermore, CA

Oct 23, 2017

Lower Elementary
Question: The 30 students in Mrs. Jackson’s class are going to the zoo. They will ride in vans that each hold 9 students. How many vans are needed to take the students to the zoo?
Answer: 4 vans
Note: They need 3 vans to take 27 students ( 9 x 3) and the 4th van holds the the other 3 students. Mrs. Jones and all other adult chaperons are able to ride in the other available seats in the van.

Upper Elementary
Question: Fred is going on a walk for charity. He earned \$1.25 for every 1/4 mile he walks. When he finished the walk, he had raised \$12.50. How far did he walk?
Answer: 2 1/2 miles
Note: If Fred raises \$1.25 for every 1/4 mile, then he earns \$5.00 each mile he walks (1.25 x 4). So he earns \$10.00 for 2 miles. To get to \$12.50, we must add another \$2.50, which is earned for 1/2 mile (2.50 = 1.25 x 2 and 2 x 1/4 = 1/2). So, to raise \$12.50, Fred would have had to walk 2 1/2 miles.

Middle School
Question: By doubling in size everyday, a lily pad can cover a pond in 10 days. How long will it take two such lily pads to cover the same pond?
Answer: 9 days
Note: If a lily pad covers the pond in 10 days by doubling everyday, then on the 9th day it is half the size of the pond. Starting on the same day and growing at the same rate, two lily pads would both be half the size of the pond on the 9th day, covering the entire pond.

Algebra and Up
Question: How much water must be added to 5 quarts of a mixture that is 75% juice to make a mixture that is 40% juice?
Answer: 4.375 quarts
Note: This is a mixture problem. We are taking something that is already 75% juice and adding water in order to make the concentration of juice go down to 40% for the new mixture. Solving mixture problems relies on parts and wholes and value x quantity. This should be set up using the following form:
(% juice)x(Amount of mixture) + (% juice)(Amount of Water) = (% juice)(Total amount of mixture plus the added water).
It is important to remember that water is 0% juice.
Let x = the amount of water added
Let x + 5 = the total amount of the new mixture
.75(5) + (0)(x) = .40(5 + x)
Multiplying the equation through by 100 we find
75(5) + 0(x) = 40(5 + x)
375 = 200 + 40x
175 = 40x
4.375 = x