The first mechanic worked for 10 hours and the second mechanic worked for 15 hours.
Step-by-step explanation:
Given,
Charges of first mechanic = $95 per hour
Charges of second mechanic = $115 per hour
Total hours = 25
Total amount charged = $2675
Let,
The number of hours worked by first mechanic = x
The number of hours worked by second mechanic = y
According to given statement;
x+y=25 Eqn 1
95x+115y=2675 Eqn 2
Multiplying Eqn 1 by 95
[tex]95(x+y=25)\\95x+95y=2375\ \ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](95x+115y)-(95x+95y)=2675-2375\\95x+115y-95x-95y=300\\20y=300[/tex]
Dividing both sides by 20
[tex]\frac{20y}{20}=\frac{300}{20}\\y=15[/tex]
Putting y=15 in Eqn 1
[tex]x+15=25\\x=25-15\\x=10[/tex]
The first mechanic worked for 10 hours and the second mechanic worked for 15 hours.
Keywords: linear equation, elimination method
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