At a school number of boys : number of girls = 9:7. There are 116 more boys than girls. Work out the total number of students at the school

Let x be a number of boys and y be a number of girls.

Then x:y=9:7, that is 7x=9y; and we have x-y=116.

Thus, x=116+y

7 (116+y) = 9y

7*116+7y=9y

2y=7*116

y=7*58=406

x=406+116=522

Total number of students is x+y=522+406=928.

X=number of boys.

y=number of girls.

we suggest this system of equation

x/y=9/7

x=y+116

We solve this system of equation by substitution method.

(y+116) / y=9/7

7 (y+116) = 9y

7y+812=9y

9y-7y=812

2y=812

y=812/2=406

x=y+116

x=406+116=522

answer: At the school there are 522 boys and 406 girls.

to chek.

522/406=1.2857 ...

9/7=1.2857 ...

The number of boys (522) is equal to 406+116=522.