A retail store employs only clerks and managers and the

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A retail store employs only clerks and managers and the clerks earn $11.50/hour while the managers earn $19/hour. Last year, the store had 20 employees and its average employee earned $13/hour. Thus far this year, the store has hired 4 clerks and promoted some of last year’s clerks to manager. If the store has undergone no other personnel changes and the average employee now earns $14/hour, how many clerks were promoted to manager?

A. 2
B. 4
C. 6
D. 7
E. 8

OA B

We can let x = the number of clerks in the store before any new hires or promotions. Thus, 20 - x = the number of managers, and we can create the equation:

(11.5x + 19(20 - x))/20 = 13

11.5x + 380 - 19x = 260

-7.5x = -120

x = 16

Therefore, there were 16 clerks and 4 managers before any new hires or promotions, and there were 24 employees after the personnel changes. Now let’s let n = the number of clerks who were promoted to manager. Since there are 4 new clerks who were hired, we can create the equation for the income of the employees:

(11.5(16 + 4 - n) + 19(4 + n))/24 = 14

230 - 11.5n + 76 + 19n = 336

7.5n = 30

n = 4

Answer: B