The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength? *​

Explanation:

If there were 7 boys and 5 girls, then we'd have the ratio of 7:5. The boys are listed first because of how your teacher mentions boys first to set up the ratio. The order is important. That means 7:5 is different from 5:7.

With 7 boys and 5 girls, we see that there are 7-5 = 2 more boys compared to girls, and not 8. The jump from 2 to 8 is "times 4", which means we'll need to multiply each gender count by 4 to get to the class size we want

boys: 7 ---> 7*4 = 28

girls: 5 ---> 5*4 = 20

Having 28 boys and 20 girls will lead to the ratio 28:20, and it reduces fully to 7:5 when we divide both parts by the GCF 4.

The total number of students is 28+20 = 48

Here's another way we can solve.

x = number of girls

x+8 = number of boys, since there are 8 more

The ratio of boys to girls is 7:5, meaning,

(number of boys)/(number of girls) = 7/5

(x+8)/x = 7/5

(x+8)*5 = x*7 cross multiply

5x+40 = 7x

40 = 7x-5x

40 = 2x

2x = 40

x = 40/2

x = 20

There are x = 20 girls and x+8 = 20+8 = 28 boys. So 20+48 = 48 total.