Company X had a ratio of 4 full-time employees for every 3 part-time

We know that the ratio of fulltime to part-time employees = 4x : 3x

After 2 part-time employees quit, the ratio is 3:2, so we have:

4x/(3x-2) = 3/2

8x = 3(3x - 2)

8x = 9x - 6

6 = x

Thus, the company now has 4(6) + 3(6) - 2 = 40 total employees.

Answer: B

Once we know that x = 6, why don't we plug that into the new ratio (3:2)? Confused as to why the new ratio isn't the current number of employees.

jsheppa , the multiplier x = 6 is for the original ratio. That is the ratio that has the mathematical "operation" performed on it.

When we have a ratio whose parts (numerator and/or denominator) change, and that change results in a different ratio, the multiplier is for the original. Its "counting number" of members changed.

Everything that happens (2 people leave, the result is a different part:part ratio) stems from the original ratio.

Thus:
\(\frac{4x}{3x}\)
\(\frac{4x}{(3x-2)}=\frac{3}{2}\)

\(8x = 9x - 6\)
\(x = 6\)

The number of original employees had to be
(4x = 24) + (3x = 18) = 24 + 18 = 42 ORIGINAL minus 2 people who left = 40 NOW

Those 40 are in a 3:2 ratio, but if you used x=6 on that ratio, you would get (3x = 18) and (2x = 12). 18 + 12 = 30.

Hope that helps.

I found the answer in a much easier way without doing much math.

You are said that before two employees leave the ratio of employees is 4:3.

This means that the total number of employees before is a multiple of 7.

All you are left to do is to add 2 (which corresponds to the number of employees that left) to each answer choice. The answer choice that is a multiple of 7 must be the right answer

Thus :
A. 30+2 = 32 Not a multiple of 7
B. 40+2 = 42 A Multiple of 7
C. 50+2 = 52 Not a multiple of 7
D. 60+2 = 62 Not a multiple of 7
E. 70+2 = 72 Not a multiple of 7

f :p
4:3
f:p
3:2
make ratios same
f:p
12:9
f:p
12:8
diff between part time is 1 but diff is 2 so multip factor is 2
12*2 + 8*2
24+16
40

If F is number of full time employees and P is number of Part time employees
F:P = 4:3

i.e. F = 4x
and P = 3x

After two employees quit, P = 3x-2

New F:P = 4x : (3x-2) = 3:2

i.e. 8x = 9x-6
i.e. x = 6

Current number of employees = 4x+3x-2 = 7x - 2 = 7*6 - 2 = 40

Answer:option B

ALTERNATIVELY:

earlier Ratio = 4:3 i.e. Before 2 employees left, Total employees was a multiple of 7

After two employees left the ratio is 3:2 i.e. Answer and final number of employees is a multiple of 5

All options are multiples of 5
But only 40 (out of all options) with addition of 2 (employees left) is a multiple of 7

Hence
Answer: Option B

Can someone gives me a heads up, what is x in the function?

4x/3x-2 = 3/2 ?

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