Answer:
At the beginning
16 men and 24 women
In the end
16 men and 20 women
Step-by-step explanation:
Call x the number of men on the bus and call y the number of women on the bus.
We know that the initial ratio between men and women is 2: 3
And the final ratio is 4: 5
So
[tex]\frac{x}{y}=\frac{2}{3}\\\\y = \frac{3}{2}x[/tex] (1)
After the 4 women are down, the proportion is:
[tex]\frac{x}{y-4}=\frac{4}{5}\\\\y-4 = \frac{5}{4}x\\\\y= \frac{5}{4}x +4[/tex] (2)
Substitute the value of y in the first equation and solve for x
[tex]\frac{5}{4}x +4=\frac{3}{2}x\\\\-\frac{1}{4}x=-4\\\\x=16\ men[/tex]
Now solve for y.
[tex]y = \frac{3}{2}(16)\\\\y=24\ women[/tex]
Then at the end there were
[tex]y = 24-4 = 20[/tex] women
