SOLUTION: 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 ki

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Question 174698This question is from textbook Alegebra 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 elimination method for each variable.
Thank You for all your help in advance. =) This question is from textbook Alegebra 2, Texas Edition

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call the time spent at soup kitchen,trash pickup, and toy collecting
s, t, and c, respectively
:
c=4t...........eq 1
s=t-2..........eq 2
s+t+c=40.......eq 3
:
:
c=4t........eq 1
s+t+c=40....eq 3
:
multiply eq 1 by -1 to then add the two equations together thus eliminating the c terms, leaving us with s+t=-4t+40---->s+5t=40
:
s=t-2.....eq 2
s+5t=40...revised equation after eliminating c terms
:
multiply eq 2 by -1 and add the two equations together thus eliminating the s terms, leaving us with 5t=-t+2+40
:
6t=42
:
highlight%28t=7%29hours picking up trash
:
highlight%28c=4t=4%287%29=28%29hours toy collecting
:
highlight%28s=t-2=7-2=5%29hours in the soup kitchen