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
A retail store employs only clerks
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Plot the initial wages on a number line: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
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
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number of employees initially = 20lheiannie07 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
average earning = $13/ hour
therefore total earning = 20 x 13 = $260/hour
later 4 more clerks are employed so total earning @ $14/hour = 24 x 14 = $336/hour
earning of the 4 new clerks @ $11.5/hour = 4 x 11.5 = $46/hour
therefore total earning of the initial 20 employees = 336 - 46 = 290/hour
therefore increase in total earning of
initial 20 employees(due to some clerks promoted to managers) = 290 - 260 = $30/hour
that is clerks promoted as managers shall get a total of $30 more
earnings increased of each clerk promoted as manager = 19 - 11.5 = $ 7.5/hour
therefore number of clerks promoted as managers = 30/7.5 = 4
so the correct answer is B
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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:BTGmoderatorDC 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
(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
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