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

Question 174551This 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 Cramer's Rule. 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
:
rewrite equations
:
s+t+c=40......eq 3
s-t+0c=-2.....eq 2
0s-4t+c=0......eq 1
:
now writing out the main matrix
:
...lets call this matrix X
:
we need to find the determinant of this matrix to begin with
:
we can choose any row or column to determine this ..I will work with column 1 since it has a zero in it
:
det X=(1) det-(1)det+0=
.....1(-1)-1(5)=-6
:
s=det s/-6 where matrix s is matrix X with the 1st column replaced by constant coefficents 40,-2,0. I will use column one for our determinant
:
det s = 40 det-(-2)det
=40(-1)+2(5)=-30
:
s=det s/-6=hours in the soup kitchen
:
:
t=det t/-6 where matrix t is matrix X with the 2nd column replaced by constant coefficents 40,-2,0. I will use row 3 for our determinant as it has 2 zeros
:
det t=0+0+(1)det=1(-42)=-42
:
t=det t/-6=hours picking up trash
:
:
c=det c/-6 where matrix c is matrix X with the 3rd column replaced by constant coefficents 40,-2,0. I will use row 3 for our determinant as it has 2 zeros
:
det c= 0-(-4)+0=4(-42)=-168
:
c=det c/-6=hours toy collecting

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