Question

A roofer earns $22 per hour for regular hours worked and $30per hour for overtime hours worked. If he puts in 40 hours of regular time during a certain week and he wishes to earn $1050, how many hours of overtime should he work?The roofer should work ___ hours of overtime.(Type an integer, proper fraction, or mixed number.)

Answer 1

Answer:

The roofer should work 5 2/3 hours of overtime.

Explanation:

Given:

Earnings for regular hours = $22 per hour

Earnings for overtime = $30 per hour

Time spent on regular hours = 40 hours

Total amount to be earned = $1050

To find:

The number of hours worked overtime

let the number of hours worked overtime = h

Earnings for regular hours (number of hours) + Earnings for overtime (number of hours) = 1050

$\begin{gathered} 22(40)\text{ +}30(h)\text{ = 1050} \\ 880\text{ + 30h = 1050} \end{gathered}$$\begin{gathered} collect\text{ like terms:} \\ 30h\text{ = 1050 - 880} \\ 30h\text{ = 170} \\ \\ divide\text{ both sides by 30:} \\ h\text{ = 170/30} \\ h\text{ = 17/3 = 5}\frac{2}{3}\text{ hours} \end{gathered}$