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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. A) How many men were on the bus? B) How many women were on the bus in the end?

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Answer:

We have m / w = 2 / 3;

Then, m / ( w - 4 ) = 4 / 5;

m = 2w / 3 and 5m = 4w - 16;

5 x ( 2w / 3 ) = 4w - 16;

10w / 3 = 4w - 16;

10w = 12w - 48;

2w = 48;

w = 24 (woman were on the bus in the beginning);

A) m = ( 2 x 24 ) / 3 = 16 (men were on the bus );

B) 24 + 4 = 28 woman were on the bus in the end;

Step-by-step explanation:

a. The number of men were on the bus is 16.

b. And, the number of women were on the bus is 28.

Given that,

  • 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.
  • Here we assume men be m and women be w.

Based on the above information, the calculation is as follows:

[tex]\frac{m}{w} = \frac{2}{3}[/tex]

[tex]\frac{m}{w-4} = \frac{4}{5}[/tex]

So,

[tex]m = \frac{2w}{3}[/tex] and  5m = 4w - 16

[tex]5 \times \frac{2w}{3} = 4w - 16\\\\\frac{10w}{3} = 4w - 16\\\\10w = 12w - 48\\\\2w = 48[/tex]

w = 24

Now

The men should be

[tex]= ( 2 \times 24 ) \div 3[/tex]

= 16

And, the women be

= 24 + 4

= 28

Therefore we can conclude that

a. The number of men were on the bus is 16.

b. And, the number of women were on the bus is 28.

Learn more: brainly.com/question/5882856

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