Simplification

Question

The basic hourly rate for a weekly paid worker is $ 80 and any hours above 40 are paid at $120. Tax is paid at a rate of 25% on any earnings above $800 a week.
Assuming hours worked per week (H) exceed 40, write an expression for net weekly wage in terms of H and then simplify it.

Answer 1

Break it into pieces that you can write expressions for.

Since there are more than 40 hours worked in the week, the full basic wage is (40)(80).

The excess hours to be paid at $120/hr is (H-40).

The overtime pay is thus (H-40)(120)

The 25% tax on the total leaves 75%, so (0.75) times the sum of basic pay & overtime is the net pay.

 

Net Pay is:

P = [(40)(80)+(H-40)(120)] (0.75)

P = (3200+120H-4800)(0.75)

P = (120H-1600)(0.75)

P = 90H-1200

 

Check:

Assume 50 hours worked in a week.

Base pay = 3200

Overtime pay = (10)(120)=1200

Gross pay = 4400

Net pay = (4400)(0.75)=3300

 

(90)(50)-1200=4500-1200=3300