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In a certain store, the ratio of part-time workers to full-time worker

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In a certain store, the ratio of part-time workers to full-time worker [#permalink]

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New post 14 Mar 2017, 02:27
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Question Stats:

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In a certain store, the ratio of part-time workers to full-time workers is 2 to 5. If 4 part-time workers were hired, then the ratio would be 3 to 5. How many workers does the store have?

(A) 11

(B) 12

(C) 21

(D) 28

(E) 35
[Reveal] Spoiler: OA

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Re: In a certain store, the ratio of part-time workers to full-time worker [#permalink]

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New post 14 Mar 2017, 07:50
My Approach
2x+5x=7x

\(\frac{2}{5}\)

+4 part time => \(\frac{3}{5}\)

1x=4

(2*4) + (5*4) = 28
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Re: In a certain store, the ratio of part-time workers to full-time worker [#permalink]

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New post 28 Nov 2017, 12:36
Hi All,

We're told that the ratio of part-time workers to full-time workers is 2 to 5. This means that:

1) The number part-time workers MUST be a multiple of 2
2) The number of full-time workers MUST be a multiple of 5
3) The total number of workers must be a multiple of 7

We're also told that IF 4 part-time workers were hired, then the ratio of part-time workers to full-time workers would be 3 to 5. We're asked for the TOTAL number of workers there are NOW (meaning before 4 part-time workers are hired).

This question can be solved in a number of different ways. Since the total number of workers is a multiple of 7 - and the answers are numbers - we can TEST THE ANSWERS. To start, we can eliminate Answers A and B (since they're NOT multiples of 7).

Let's TEST Answer D: 28 total workers

IF.... there are 28 total workers
8 are part-time and 20 are full-time
Adding 4 more part-time workers would give us....
12 part-time and 20 full-time
12:20 = 3:5
This is an exact match for what we were told, so this MUST be the answer!

Final Answer:
[Reveal] Spoiler:
D


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In a certain store, the ratio of part-time workers to full-time worker [#permalink]

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New post 28 Nov 2017, 13:05
vikasp99 wrote:
In a certain store, the ratio of part-time workers to full-time workers is 2 to 5. If 4 part-time workers were hired, then the ratio would be 3 to 5. How many workers does the store have?

(A) 11

(B) 12

(C) 21

(D) 28

(E) 35

Another approach: set up the original ratio with x, add the number given, set it equal to the new ratio, and multiplier x gives you the original actual numbers.

The ratio of part-time workers to full-time workers is 2 to 5

\(\frac{Part-time}{Full-time}=\frac{2x}{5x}\)

If 4 part-time workers were hired, then the ratio would be 3 to 5:

\(\frac{2x + 4}{5x}=\frac{3}{5}\)

\(5(2x + 4) = 3(5x)\)
\(10x + 20 = 15x\)
\(20 = 5x\)
\(x = 4\)


x is the multiplier for the original ratio

How many workers (TOTAL)?
Part-time = 2x = (2)(4) = 8
Full-time = 5x = (5)(4)= 20

20 + 8 = 28

Answer D

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In a certain store, the ratio of part-time workers to full-time worker   [#permalink] 28 Nov 2017, 13:05
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