lheiannie07 wrote: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
Can experts show me the best solution in this problem?
OA B
Plot the initial wages on a number line:
11.50-------13------------------19
Gap:----
1.5------------
6--------
First notice that the average is much closer to the low end than the high, so we know there are more clerks than managers. Next, if we examine the difference between each respective group and the overall average, we can see that there's a ratio of 6:1.5, or 4:1, meaning that for every 4 clerks, there will be 1 manager.
Number of clerks: 4x
Number of managers: x
Total employees: 20
4x + x = 20 --> 5x = 20--> x = 4.
Number of clerks: 4*4 = 16
Number of managers: 4.
If 4 clerks are added, there will be 20 clerks and 4 managers, and a total of 24 employees.
Next we're told that the average pay rose to 14. Again let's plot the figures on the number line
11.50---------14------------------19
Gap:----
2.5------------
5--------
Ratio of clerks : managers = 5:2.5 = 2:1.
If there are 24 employees, now we have
Clerks: 2y
Managers: y
Total 24
2y + y = 24 --> 3y = 24 --> y = 8.
Clerks:16 and Managers: 8.
If we previously had 20 clerks and 4 managers, and now we have 16 clerks and 8 managers, then 4 clerks must have been promoted. The answer is
B
