EricKryk 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
2) An increase of $1.50 would represent an increase of 20 percent of her 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
Thus, we have:
(30 – h)(w + 1.5) = 30w
We need to determine a value for h. Thus, if we can determine the value of w, 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.
Answer: D
