The ratio of the number of men to the number of women on a bus was 2 : 3. at a bus stop, 4 women got off and the ratio became 4 : 5. a) how many men were on the bus? b) how many women were on the bus in the end? i know this question was already asked on here but that answer made no sense whatsoever. if possible, explain as clear as possible and with as many words as possible.

Hello from MrBillDoesMath!

men = 16, women = 24

Discussion:

Let m = # of men of bus and w = # of women on bus.

The ratio of men to women was 2:3. That is

m/w = 2/3       (*)

Four women got off the bus, meaning that the number of women is now w-4. The ratio of men to women also changed to 4./5. This means that

m/(w-4) = 4/5  (**)

the rest is all algebraic manipulation. Multiply both sides of (*) for 3w to get

(m/w) (3w) = (2/3)(3w) =>

3m = 2w.

Multiply both sides of (**) by 5 * (w-4) to get

(m/(w-4) ) 5 (w-4) = (4/5) 5 (w-4)  =>

5m = 4 (w-4) = 4w - 16  But 3m = 2w from above so by substitution

5m =  6m - 16 =>                 (as 4w = 6m)

m = 16

As 2w = 3m = 3(16) = 48, w = 24.

Regards,  

MrB

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