jsheppa wrote:

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.

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