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?

Question

Someone already answered it using Algebra method, but I would like to know how to solve it using bar/tape model or anything similar, basically sticking to ratio solving method and not Algebra. Thanks!

Answer 1

To solve this problem, let's assume the original number of men was 2x and the original number of women was 3x, where x is some number.The original ratio of men to women was 2:3, which can be written as:

2x / 3x = 2/3At the bus stop, 4 women got off, so the new number of women became 3x - 4.The new ratio of men to women is 4:5, which can be written as:

2x / (3x - 4) = 4/5Now, let's solve this equation:

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

1. x = 8Therefore, the original number of men was 2x = 2 * 8 = 16, and the original number of women was 3x = 3 * 8 = 24.After 4 women got off, the new number of women became 24 - 4 = 20.So, the final answer is:There were 16 men on the bus
2. There were 20 women on the bus