Question

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

Answer 1

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.

Answer 2

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.