Question

The ratio of girls to boys
in a class is 14:11. If 8
boys leave and an equal
neember of guels join the
ratio changes to 3:2, find.
the total students in the class.​

Answer 1

Given:

The ratio of girls to boys  in a class is 14:11

If 8  boys leave and an equal  number of girls join the  ratio changes to 3:2

To find:

The total no. of students in the class

Solution:

Let the no. of girls in the class be "14x" and no. of boys in the class be "11x".

So,

After 8 boys left, remaining no. of boys in the class = 11x - 8

After 8 girls joined, the new no. of girls in the class = 14x + 8

The new ratio becomes 3:2

Now, we can form an equation as,

$\frac{14x \:+\: 8}{11x\:-\:8} = \frac{3}{2}$

$\implies 2(14x \:+\:8) = 3(11x\:-\:8)$

$\implies 28x \:+\:16 = 33x\:-\:24$

$\implies 24 \:+\:16 = 33x\:-\:28x$

$\implies 40 = 5x$

$\implies x = \frac{40}{5}$

$\implies x = 8$

∴ $14x = 14\times 8 = 112$

and

∴ $11x = 11\times 8 = 88$

∴ The total no. of students in the class = 112 + 88 = 200

Thus, there are 200 students in the class.

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Also View:

Ratio between the girls and boys in a class of 40 students is 2:3 five new students joined the class how many of them must be boys so that the ratio between girls and boys becomes 4:5?

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In a class of 49 students, the ratio of girls to boys is 4:3.if 4 girls leave the class, the ratio of girls to boys would be how much?

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Answer 2

Step-by-step explanation:

14x +8

11x -8

2(14x+8) = 3(11x-8)

28x+16=33x-24

24+16=33x-28x

40=5x

x=40/5

x=8

2*8=16

3*8=24