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Carmen currently works 30 hours per week at her part-time

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Carmen currently works 30 hours per week at her part-time [#permalink]

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Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?

(1) Her gross weekly pay is currently $225.00.
(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage.


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SOLUTION:

Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?

Let \(w\) be Carmen's gross hourly wage and \(t\) be the number of hours fewer Carmen will need to work. We need to find such \(t\) that \(30w=(30-t)(w+1.5)\).

(1) Her gross weekly pay is currently $225.00 --> \(30w=225\) --> we can find \(w\), so in \(30w=(30-t)(w+1.5)\) we'll be left with only one unknown: \(t\), which means that we can solve for it. Sufficient.

(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage --> \(1.5=0.2w\). The same here: we can find \(w\), so we can find \(t\). Sufficient.

Answer: D.
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Re: Carmen currently works 30 hours per week at her part-time [#permalink]

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New post 22 Aug 2013, 02:48
Hi,

I have a query with this question.

From option 1, after solving, we get that the new number of hours is 25 i.e, 5 hours less.

Option 2 states, that there was a 20% inc in the per hour wage. Can we use the concept of ratios here.
To keep total wage constant, if we increase per hour wage by 20%, we need to decrease the number of hours worked by 20% too.
=> New No. of Hours worked = 30-20%(30)= 24
This option does not provide the same answer as 1. Can you please explain the reason why ?
The relation used : Total Wage/month = No. of Hours worked * Wage/Hour

Thanks,
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Re: Carmen currently works 30 hours per week at her part-time [#permalink]

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New post 10 Jan 2014, 08:07
Bunuel wrote:
Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?

(1) Her gross weekly pay is currently $225.00.
(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage.


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Question: 28
Page: 277
Difficulty: 650



We are initally given the equation x*30 = Total Salary, and then the question is if we can solve (x + 1.5) * 30 = Total Salary, so we have two unknown values we need to solve for

1) Solves total salary, so now we have one equation and one unknown, which means 1 is sufficient.
2) Gives us the ability to solve for x, so now we have one equation and one variable (Total salary), this is also sufficient.

So, D.

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Re: Carmen currently works 30 hours per week at her part-time [#permalink]

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Bunuel wrote:
Carmen currently works 30 hours per week at her part-time job. If her gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?

(1) Her gross weekly pay is currently $225.00.
(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage.



We are given that Carmen works 30 hours per week and that her wage is to increase by $1.50 per hour. We must determine how many fewer hours she could work and still earn the same gross weekly pay as she earned before the increase. We can set up an equation to determine how many fewer hours she could work. We can let:

h = the reduction in hours, and then (30 – h) = the reduced number of hours she could work

w = Carmen’s current hourly wage and then (w + 1.5) = Carmen's hourly wage after her raise

Using the general equation that (hours) x (hourly wage) = total gross pay, we have:

(30 – h)(w + 1.5) = 30w

We need to determine a value for h. Thus, if we can determine the value of either w or h, we can answer the question.


Statement One Alone:

Her gross weekly pay is currently $225.

With the information from statement one, we know that:

30w = 225

w = 7.5

Since we have a value for w, we can substitute in to the equation, (30 – h)(w + 1.5) = 30w, and determine h.

(30 – h)(7.5 + 1.5) = 30(7.5)

(30 – h)(9) = 225

30 – h = 25

h = 5

Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

An increase of $1.50 would represent an increase of 20 percent of her gross hourly wage.

We can translate statement two into an equation:

1.5 + w = 1.2(w)

1.5 = 0.2w

1.5/0.2 = w

15/2 = w

7.5 = w

Since we know w = 7.5, we know that we can determine the value of h. Statement two is also sufficient to answer the question.

The answer is D.
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Re: Carmen currently works 30 hours per week at her part-time   [#permalink] 25 May 2017, 12:23
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