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Sagot :
We know that the total cost is $1700 and the total work hours are 15.
We will call x the number of hours worked by the first mechanic and y the number of worked hours by the second mechanic.
The total work hours is the sum of x and y and equal to 15:
[tex]x+y=15[/tex]The cost of each mechanic is the price per hour multiplied by the work hours, so we can write:
[tex]115\cdot x+110\cdot y=1700[/tex]We have a system of linear equations.
We will solve it by substitution.
[tex]x+y=15\longrightarrow y=15-x[/tex][tex]\begin{gathered} 115x+110y=1700 \\ 115x+110(15-x)=1700 \\ 115x+1650-110x=1700 \\ 115x-110x=1700-1650 \\ 5x=50 \\ x=\frac{50}{5} \\ x=10 \end{gathered}[/tex][tex]y=15-x=15-10=5[/tex]Answer: the first mechanic worked 10 hours and the second mechanic worked 5 hours.
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