MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

"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.
A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D EACH statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient."Answer:Option DEACH statement ALONE is sufficient.
Solution:Given that, Carmen currently works 30 hours per week at her part-time job. Her gross hourly wage were to increase by $1.50, We have to find how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase?
Now, we are also given that,
(1)Her gross weekly pay is currently $225.00. Let her hourly wage be $n.
Now, from 1 ⇒ her weekly payment = $225[tex]\begin{array}{l}{\rightarrow \text {Number hours worked } \times \text {hourly wage }=225} \\\\ {\rightarrow 30 \times n=225} \\\\ {\rightarrow 10 \times n=75} \\\\ {\rightarrow 2 n=15} \\\\ {\rightarrow n=7.5} \\\\ {\text {So her hourly wage is } \$ 7.5}\end{array}[/tex]Now, after increasing the hourly age by 1.5 her hourly wage will be 7.5 + 1.5 = $9
And let the new number of hours required needed to work to get the same weekly wage be m hours.
[tex]\begin{array}{l}{\text {Then, } m \text { hours } \times \$ 9 \text { per hour }=\$ 225} \\\\ {\rightarrow m \times 9=225} \\\\ {\rightarrow m=25}\end{array}[/tex]So, she has to work work 25 hours to get the same amount.
(2) An increase of $1.50 would represent an increase of 20 percent of her current gross hourly wage. Let the hourly wage be $ “a”[tex]\text { Then, } 20 \% \text { of } a=\$ 1.5 \rightarrow \frac{20}{100} \times a=1.5 \rightarrow 20 a=150 \rightarrow a=\$ 7.5[/tex]Here, we got hourly wage from 2, which means we can obtain the new working time again by using the same process used in 1.
Hence, both statements are alone sufficient to solve the question. So option D is correct.