Answer: There are 324 boys and 32 girls in the eight grade at Euclid’s middle school.
Step-by-step 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 :
[tex]x+y=356----(1)\\\\ 34+4y=\dfrac{1}{2}x----(2)[/tex]
Simplifying (2)
[tex]x=2(34+4y)\\\\ x=68+8y-----(3)[/tex]
Substitute the value of x from (3) to (1), we get
[tex]68+8y+y=356\\\\ 9y=356-68\\\\ 9y=288\\\\ y=\dfrac{288}{9}=32[/tex]
Put y=32 in (3), we get
[tex]x=68+8(32)=324[/tex]
Hence, the number of boys = 324 and the number of girls = 32
