ratio

"at a school number of boys:number of girls=11:9

there are 124 more boys than girls

work out the total number of students at the school"

b/g = 11/9    so  b = 11g/9

g + 124 = b     so  g + 124 = 11g/9   Multiply both sides by 9

9g + 9*124 = 11g     subtract 9g from both sides

9*124 = 2g    divide both sides by 2

g = 9*124/2   or g = 9*62   so  g = 558

Hence b = 558+124   or  b = 682

Total students = 558 + 682 = 1240

.

Total number of students=S
Number of girls =G
Number of Boys =G+124
G+G+124 = S
11/20S =G+124, solve for G, S
G=558 - Number of girls.
S =1,240 - Total number of students
1,240 - 558 =682 - Number of boys.