Question

Julio is paid 1.4 times his normal hourly rate for each hour he works over 30 hours in a week. Last week he worked 35 hours and earned $436.60. Write and solve an equation to find Julio's normal hourly rate, r. Explain how you know that your answer is reasonable.

Answer 1

n = regular rate
1.4n= overtime rate

30n + 5(1.4n) = $436.60 (30 hours x regular rate n) plus 5 hours at 1.4 times reg rate.

30n + 7n = $436.60 now add like terms
37n = $436.60 now divide both sides by 37
n= $11.80
Check to see if my answer is reasonable 30 x 12= 360 + 5 x 10 x 1.4 = about 70 (notice that I used 10 instead of 12 here so I could do it in my head)
360 + 70 = 430 - close enough - my answer is reasonable
Check:
(30 x $11.80) + 5 ( 1.4 x 11.80
354 + 5( 16.52)
354 + 82.60 = 436.60 ($436.60)

Answer 2

Normal earning rate of Julio is $11.78

Explanation:

Let the normal hourly rate of earning = $r per hour

Then for overtime earnings = 1.4 × $r per hour

Julio works for 30 hours so earnings = 30(r)

last he did overtime for 5 hours (35 - 30) so the earning for the overtime = 5(1.4r) = 7r

Total earning of Julio = 30r + 7r = $436

or 37r = $436

r =
`(436)/(37)` = $11.78

Therefore, normal rate of Julio's earning is $11.78.