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A yard cleanup service charges a $254 fee plus $19.25 per hour. Another cleanup service charges a $133 feeplus $24.75 per hour. How long is a job for which the two companies' costs are the same?

A yard cleanup service charges a $254 fee plus $19.25 per hour. Another cleanup service-example-1

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The first thing we have to do is identify the 2 equations that describe our problem

CS = Cleanup servise

h = hour


CS_1=254+19.25h
CS_2=133+24.75h

If we want to know how many hours must be worked so that both services cost the same, we must equalize the equations


\begin{gathered} 254+19.25h=133+24.75h \\ 24.75h-19.25h=254-133 \\ 5.5h=121 \\ h=(121)/(5.5) \\ h=22 \end{gathered}

The answer is 22 hours

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