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.
