Question

There are 356 eighth-grade students at Euclid’s Middle school. Thirty four more than four times the number of girls is equal to half the number of boys. How many boys are in eight grade at Euclid’s middle school? How many girls?

Answer 1

Answer: There are 324 boys and 32 girls in the eight grade at Euclid’s middle school.

Explanation:

Let x be the number of boys and y be the number of girls in the Euclid’s Middle school.

As per given , we have the following system of equations :

`x+y=356----(1)\\\\ 34+4y=(1)/(2)x----(2)`

Simplifying (2)

`x=2(34+4y)\\\\ x=68+8y-----(3)`

Substitute the value of x from (3) to (1), we get

`68+8y+y=356\\\\ 9y=356-68\\\\ 9y=288\\\\ y=(288)/(9)=32`

Put y=32 in (3), we get

`x=68+8(32)=324`

Hence, the number of boys = 324 and the number of girls = 32