At a grocery store, Mike normally works 7.5 hours per day and earns x

Question

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

A. 3.5
B. 4.5
C. 6
D. 6.5
E. 7

generis · Answer

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

vipulshahi · Answer

For Mike, Rate = 7.5hrs/day
Earn = $x/hrs

Let suppose the number of hours Mike worked on daily basis = n

So total income for the day = 7.5* x 
Now he wants to double the earning so now the equation becomes,
=> 7.5 * x + (n-7.5) * 1.25 * x = 2 * 7.5* x
=> 1.25 * x * n - 7.5 * 1.25 * x = 7.5 * x
=> 1.25n - 7.5 * 1.25 = 7.5
=> 1.25n = 7.5 + 7.5*1.25
=> 1.25n = 7.5( 2.25)
=> n = 7.5 * 2.25 / 1.25
=> n = 7.5 * 225 / 125
=> n = 7.5 * 45/25
=> n = 7.5 * 9 / 5
=> n = 1.5 * 9
=> n = 13.5
 
Hence , Excess hours Make will work = 13.5 - 7.5 = 6

Answer : 6 (C)

Skaa · Answer

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
Solve by substituting values for the amount earned by Mike per hour 
Therefore, x = 10
7.5 X 10 = 75 ( per day)
So Mike needs to make another 75. 
For every extra hour he is paid 1.25 times his regular rate
So, 10 x 1.25 = 12.5
To make the additional 75: 75= 12.5 X no. of hours
No. of hours = 6

Answer (C)

bumpbot · Answer

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At a grocery store, Mike normally works 7.5 hours per day and earns x

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