Answer:
16 men
20 women
Step-by-step explanation:
We are given that the ratio of the number of men to the number of women on a bus was 2:3 at a bus stop.
So assuming x to be the number of persons (male or female), we can write it as:
[tex] \frac {2x}{3x}[/tex]
When 4 women got off the bus, the ratio changed to 4:5.
[tex] \frac {2x} {3x-4} = \frac {4} {5}[/tex]
Solving it to find x:
[tex]5(2x)=4(3x-4)[/tex]
[tex]10x=12x-16[/tex]
[tex]2x=16[/tex]
[tex]x=8[/tex]
So, number of men on the bus = [tex]2(8)[/tex] = 16
and number of women on the bus at the end = [tex]3(8)-4 = 24-4[/tex] = 20
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 20 women (because 4 women got off the bus)
