ratio word problems using 4 steps?

Question

When Adam and Megan arrived at a party the ratio was 1 adult to every 4 kids. But 30 more boys came Megan noticed the the ratio was now 2 boys to 1 girl. Then 30 more girls came now the ratio 4 girls to 3 boys. What is the final ratio od adult chaperones to kids?

Answer 1

Let a, b and g be the no. of initial adults, boys and girls respy. Then a/(b+g)=1/4 (Equation 1)
When 30 boys come in, the total would be b+30 boys and g girls. It is given that (b+30)/g=2/1 or 2g=b+30 (Equation 2)
When 30 girls join the group, the total would be b+30 boys already existing and g+30 girls. It is given that
(g+30)/b+30)=4/3, or 3(g+30)=4(b+30) or 3g=4b+30 (Equation 3)
Solving equations 2 and 3, we get b=6, g=18.
Substituting in equation 1, a=24/4=6.
The current ratio of adults to kids is a/{(b+30)+(g+30)}
=6/84=1/14. The final ratio of adults to kids is therefore 1 adult for 14 kids.
EDIT
The above explanation is descriptive. You can make it into 4 steps with a little bit of effort.