Bunuel wrote:

At a grocery store, Mike normally works 7.5 hours per day and earns x dollars per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.25 times his regular rate. If Mark suddenly decides to start working over time, how many over time hours should he work to double his daily income on a given day?

A. 3.5

B. 4.5

C. 6

D. 6.5

E. 7

Regular daily income: (# of regular hrs) *(rate/hr)

Let x = regular wage per hour

Regular daily income is 7.5 hrs * x dollars/hr = 7.5x dollars

Doubled daily income?

To double daily income, he needs an additional 7.5x dollars --

not 15x dollars. He already earns 7.5x dollars from regular time at regular pay.

So, from overtime hours worked, he must earn 7.5x dollars total

(# overtime hours)*(1.25x dollars/hr) must = 7.5x

Overtime

rate = 1.25x dollars per hour

Let y = # of overtime hours

y * 1.25x = 7.5x

y = \(\frac{7.5x}{1.25x}= 6\) hours of overtime

ANSWER C

OR: Assign values

Let regular hourly wage, x = $20 per hour

Regular income per day: 7.5 hrs * $20/hr = $150

To double daily income, he needs another $150 (he already earns $150 from regular time)

(# of overtime hours) * (increased rate per hour) must = $150

Overtime wage/hr is 25 percent more than regular wage: $20 * 1.25 = $25 per OT hour

Let y = number of overtime hours

$25 * y = $150

y = \(\frac{$150}{$25}=\) 6 hours of overtime

Answer C

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