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Question 174452This question is from textbook Algebra 2, Texas Edition
: 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.
Please help and try to show every bit of work that you can to help me better understand the problem, Thank You! =)
This question is from textbook Algebra 2, Texas Edition
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 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)
.
collecting toys:
4x = 4(7) = 28 hours
.
soup kitchen:
x-2 = 7-2 = 5 hours
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