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02 Jan 2018, 01:25
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C
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81% (02:07) correct
19%
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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
02 Jan 2018, 08:53
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Bunuel
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
03 Jun 2020, 01:08
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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)
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)
