Answer:
There are 324 boys and 32 girls in grade 8 at Euclid's middle school.
Explanation:
Let's break down the information provided to solve for the number of boys and girls in grade 8. Let's assume the number of boys in grade 8 is represented by "b" and the number of girls is represented by "g."
From the given information:
"Thirty-four more than four times the number of girls is equal to half the number of boys":
4g + 34 = (1/2)b
"There are 356 grade 8 students":
b + g = 356
Now we have a system of two equations with two variables. We can solve this system to find the values of b and g.
Using equation 2, we can rewrite it as:
b = 356 - g
Substituting this value in equation 1:
4g + 34 = (1/2)(356 - g)
Multiplying both sides by 2 to eliminate the fraction:
8g + 68 = 356 - g
Combining like terms:
9g + 68 = 356
Subtracting 68 from both sides:
9g = 288
Dividing both sides by 9:
g = 32
Now we can substitute the value of g back into equation 2 to find the value of b:
b + 32 = 356
b = 356 - 32
b = 324
Therefore, there are 324 boys and 32 girls in grade 8 at Euclid's middle school.