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Ryan is working twopart time jobs for 25 hours a week. Job A pays 6.50 and hour and job B pays 6.90. How many hours did he work in order to make $167.70

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2 Answers

Let x = the number of hours that Ryan works on job A.  Since Ryan works 25 hours total, the number of hours he works on job B is 25 - x.  We want:
 
x*($6.50) + (25-x)*($6.90) = $167.70
 
(6.5)x + 172.5 - (6.9)x = 167.7
 
-(0.4)x = -4.8
 
x = 12 hours on job A
 
So Ryan works 25 - 12 = 13 hours on job B
We have a system of equations
a + b = 25
6.50a + 6.90b = 167.70
 
isolate a
a + b - b = 25 - b
a = 25 - b
 
Use substitution to find b
6.50(25-b) + 6.90b = 167.70
162.50 - 6.50b + 6.90b = 167.70
162.50 + 0.4b - 162.50 = 167.70 - 162.50
(1/0.4) 0.4b = 5.2 (1/0.4)
b = 13
 
a = 25 - 13
a = 12
 
6.50(12) + 6.90(13) = 167.70
78.00 + 89.70 = 167.70
167.70 = 167.70