Question

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?

Answer 1

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

$\begin{gathered} 254+19.25h=133+24.75h \\ 24.75h-19.25h=254-133 \\ 5.5h=121 \\ h=\frac{121}{5.5} \\ h=22 \end{gathered}$

The answer is 22 hours