find the wages for 50 hours of work, using \double - time\ overtime pay after 40 hours. overtime pay hours…

Explanation:

Step1: Calculate regular - rate per hour

The regular - rate is calculated for the first 40 hours. Since for 40 hours of work, the money earned is $520, the regular - rate per hour $r=\frac{520}{40}=13$ dollars per hour.

Step2: Calculate overtime hours

The total hours worked is 50 hours. The overtime hours $h = 50 - 40=10$ hours.

Step3: Calculate overtime rate per hour

The overtime rate is double - time, so the overtime rate per hour $R = 2r$. Since $r = 13$, then $R=2\times13 = 26$ dollars per hour.

Step4: Calculate overtime pay

The overtime pay $P_{o}=R\times h$. Substituting $R = 26$ and $h = 10$, we get $P_{o}=26\times10 = 260$ dollars.

Step5: Calculate total pay

The pay for the first 40 hours is $P_{40}=520$ dollars. The total pay $P=P_{40}+P_{o}$. Substituting $P_{40}=520$ and $P_{o}=260$, we get $P = 520+260=780$ dollars.

Answer:

$780$