Question

sonya, who is paid time - and - a - half for hours worked in excess of 40 hours, had gross weekly wages of $800 for 56 hours worked. what is her regular hourly rate? sonyas regular hourly rate is $\square$ per hour.

Explanation:

Step1: Define variables

Let \( r \) = regular hourly rate (in dollars).

Step2: Calculate overtime hours

Overtime hours = Total hours - 40 = \( 56 - 40 = 16 \) hours

Step3: Set up wage equation

Regular pay + Overtime pay = Total gross pay
\( 40r + 16\times1.5r = 800 \)

Step4: Simplify overtime term

\( 16\times1.5r = 24r \), so equation becomes:
\( 40r + 24r = 800 \)

Step5: Combine like terms

\( 64r = 800 \)

Step6: Solve for \( r \)

\( r = \frac{800}{64} = 12.5 \)

Answer:

Sonya's regular hourly rate is $\boldsymbol{12.5}$ per hour.