Question

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. 1 How many men were on the bus? b. How many women were on the bus in the end?

Answer 1

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:

$\frac {2x}{3x}$

When 4 women got off the bus, the ratio changed to 4:5.

$\frac {2x} {3x-4} = \frac {4} {5}$

Solving it to find x:

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

$10x=12x-16$

$2x=16$

$x=8$

So, number of men on the bus = $2(8)$ = 16

and number of women on the bus at the end = $3(8)-4 = 24-4$ = 20

Answer 2

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

$\frac{x}{y}=\frac{2}{3}\\\\y = \frac{3}{2}x$   (1)

After the 4 women are down, the proportion is:

$\frac{x}{y-4}=\frac{4}{5}\\\\y-4 = \frac{5}{4}x\\\\y= \frac{5}{4}x +4$   (2)

Substitute the value of y in the first equation and solve for x

$\frac{5}{4}x +4=\frac{3}{2}x\\\\-\frac{1}{4}x=-4\\\\x=16\ men$

Now solve for y.

$y = \frac{3}{2}(16)\\\\y=24\ women$

Then at the end there were 20 women  (because 4 women got off the bus)