ratio question

Question

The ratio of the number of men to the on a bus was 2:3. At a bus stop, 4 women got off and the ratio became 4:5. How many men were on the bus and how many women were on the bus?

Answer 1

ratio of men to women is 2:3

this doesn't mean that there are only 2 men and 3 women

there could be:

2 men and 3 women

4 men and 6 women

6 men and 9 women

and so on

2 and 3 have to be multiplied by some number, call it x, to determine the exact number of men and women

2x/3x is how to write the ratio

4 women got off the bus

2x is the number of men and 3x-4 is the number of women

2x/(3x-4) is the ratio now which equals 4/5

2x/(3x-4)=4/5

cross multiply

5*2x=4*(3x-4)

10x=12x-16

10x-12x=-16

-2x=-16

2x=16

x=16/2

x=8

2*8=16 and 3*8=24, so the original ratio was 16/24 which is 2/3

4 women got off the bus

16 men and 24-4=20 women

16/20=4/5

16 men were on the bus and 24 women were on the bus