166k views
2 votes
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?

2 Answers

2 votes

Answer:

At the beginning

16 men and 24 women

In the end

16 men and 20 women

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


(x)/(y)=(2)/(3)\\\\y = (3)/(2)x (1)

After the 4 women are down, the proportion is:


(x)/(y-4)=(4)/(5)\\\\y-4 = (5)/(4)x\\\\y= (5)/(4)x +4 (2)

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


(5)/(4)x +4=(3)/(2)x\\\\-(1)/(4)x=-4\\\\x=16\ men

Now solve for y.


y = (3)/(2)(16)\\\\y=24\ women

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

User Taras Lukavyi
by
8.9k points
2 votes

Answer:

16 men

20 women

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

User Alamgir Qazi
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories