Question 174452
As a participant in your school's community service project, you volunteer a total of 40 hours over the course of the school year. Your volunteer hours include serving at a soup kitchen, picking up trash at several local parks, and collecting toys for needy children. You spend 4 times as many hours collecting toys as picking up trash, and 2 hours less serving at the soup kitchen than picking up trash.
1. Write a system of equations to represent the given information and solve using the substitution method.
.
Let x = hours spent picking up trash
then from: "You spend 4 times as many hours collecting toys as picking up trash"
4x = hours collecting toys
and from: "2 hours less serving at the soup kitchen than picking up trash"
x-2 = hours serving at the soup kitchen
.
Then because the total volunteer hours were 40:
40 = (x) + (4x) + (x-2)
40 = x + 4x + x - 2
40 = 6x - 2
42 = 6x
7 hours = x (time picking up trash)
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collecting toys:
4x = 4(7) = 28 hours
.
soup kitchen:
x-2 = 7-2 = 5 hours