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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. thanks!

1 Answer

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Hello from MrBillDoesMath!

Answer:

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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