What is the algorithm for: 4/7 of a group are boys, if there are 18 more boys than girls, how many children altogether?

Question

We were able to create a visual model and came to the answer of 126, I am having a hard time knowing how to build the algorithm. Help is appreciated.

Answer 1

g=# of girls

g+18=# of boys

2g+18=total # of people

(4/7)(2g+18)=g+18

(8g/7)+(72/7)=g+18

(8g/7)-g=18-(72/7)

(g/7)=18-10 2/7

(g/7)=7 5/7

(g/7)=54/7

7(g/7)=7(54/7)

g=54 girls

g+18=72 boys

54+72=126 children