Math Problem Monday - Jan 6th, 2020 | Mathnasium Livermore, CA

Jan 6, 2020 | Livermore

Lower Elementary
Question: At the beach, Sally found 24 seashells, Jenny found 18 seashells, and Robert found 21 seashells. How many seashells did they find altogether?
Answer: 63 shells
Solution: Because we want to find the total number of seashells Sally, Jenny, and Robert found, we add the number of seashells found together.
24 + 18 + 21 = 63 shells

Upper Elementary
Question: An average school bus is 39 feet long. The world’s largest mammal, the blue whale is approximately 2 and a half times longer than the average school bus. How long is a blue whale?
Answer: 97½ feet
Solution: To find the length of a blue whale, we multiply 39 by 2 and a half. First multiply 39 by 2. Because multiplying by a half means to take half of the number, we add half of 39 to 78 (39 x 2).
39 x 2½ = 39 x 2 + half of 39 = 78 + 19½ = 97½

Middle School
Question: It takes the earth 23.934 hours to make a complete rotation around its axis. If the circumference of the earth at its equator is 24,901.55 miles, how fast, in mph, does the earth spin? (Round answer to the nearest tenth)
Answer: 1040.4 mph
Solution: To solve this problem we need to do is divide 24,901.55 miles by 23.934 hours.
24,901.55 miles ÷ 23.934 hours
Before we can divide we need to make the devisor, 23.934, into a whole number. So we multiply both the divisor and the dividend (24,901.55) by 1000.
1000(24,901.55 miles) ÷ 1000(23.934 hours)
24,901,550 miles ÷ 23,934 hours ≈ 1040.4 miles/hour

Algebra and Up
Question: 6 paint brushes and 2 gallons of paint cost $21.00. 3 paint brushes and 4 gallons of paint cost $28.50. How much does 1 paint brush and 1 gallon of paint cost?
Answer: $7.50
Solution: Let b stand for the cost of 1 paint brush and p stand for the cost of 1 gallon of paint. Because we have 2 unknown variables (b and p) we need two equations to solve for both.
“6 paint brushes and 2 gallons of paint cost $21.00” can be represented algebraically as:
6b + 2p = 21.00 (1)
and “3 paint brushes and 4 gallons of paint cost $28.50” can be represented algebraically as:
3b + 4p = 28.50 (2)
There are 2 ways to solve a system of equations, by the substitution method and by the elimination method. Because 6b and 3b are multiples of each other, the easiest way to solve the system is by using the elimination method.
Using the elimination method, solve for p

       6b + 2p = 21.00
+ –2(3b + 4p = 28.50)
             –6p = –36.00
               p = 6

Because a gallon of paint (p) cost $6.00 we substitute this for equation 1 or equation 2 to solve for the cost of a single brush (b).

Using equation 1:
6b + 2(6) = 21.00
6b + 12 = 21.00
6b = 9.00
b = 1.50

Using equation 2:
3b + 4(6) = 28.50
3b + 24 = 28.50
3b = 4.50
b = 1.50

Finally we add $6.00 and $1.50 to get a total cost of 1 paint brush and 1 gallon of paint to be $7.50.

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