Let's use g to represent girls and b to represent boys.
b + 50 = g
This is because the amount of girls is 50 more than the amount of boys.
b + g = 1398
This is because the total number of students is 1398.
Now we have a system of equations.
{ b + 50 = g
{ b + g = 1398
To solve this, plug the expression equal to g, which is b + 50, in for g in the second equation.
b + g = 1398
g = b + 50
b + (b + 50) = 1398
Since this equation only uses addition and the order of addition doesn't affect the outcome, we can remove the parentheses.
b + (b + 50) = 1398
b + b + 50 = 1398
Now combine like terms.
b + b + 50 = 1398
b + b = 2b
2b + 50 = 1398
Now isolate the variable.
2b + 50 = 1398
First, subtract 50 from both sides.
2b + 50 - 50 = 2b
1398 - 50 = 1348
2b = 1348
Now divide both sides by 2.
2b / 2 = b
1348 / 2 = 674
b = 674
b = 674
This means there are 674 boys in Central High School.
Since b + 50 = g, plug in the now-known value of b, being 674, in for the variable and solve.
b + 50 = g
b = 674
674 + 50 = g
674 + 50 = 724
g = 724
g = 724
This means there are 724 girls in Central High School.
b = 674
g = 724
This means there are 674 boys and 724 girls in Central High School.
Now just check the answer.
b + g = 1398
674 + 724 = 1398
1398 = 1398, so this answer is correct.
Final answers:
b = 674
g = 724
There are 674 boys and 724 girls in Central High School.
Hope this helps!
