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 174516This 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. Solve this system of equations using the elimination and Cramer's Rule Method. This question is from textbook Algebra 2, Texas Edition

Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
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! =)
:
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
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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
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s=t-2.....eq 2
s+5t=40...revised equation after eliminating c terms
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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
:
hours picking up trash
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hours toy collecting
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hours in the soup kitchen