I’m having Trouble figuring out this question about ratios.

Question

In a Cafeteria, The ratio of Girls to Boys is 4:3. when 4 girls leave, The Ratio of girls to boys is 11:9. How many girls were in the Cafeteria Originally?

Answer 1

4/3 = G/B G=original number of girls, B=original number of boys

(G-4)/B = 11/9 when 4 girls leave, the ratio gets

cross multiply in each equation to get

4B =3G and 9(G-4)=11B

9G-36 = 11B Multiply 4B=3G by 3 to get 12B=9G

9G=11B+36 and 9G=12B

set them equal to get 12B=11B+36 subtract 11B from both sides to get

B=36 the original number of boys

4/3 = G/B or 4/3 =G/36

cross multiply to get

3G=4(36)=144

G=144/3 = 48 original girls

G=48, B=36

G=36+12 G is 12 larger

when 4 girls left G=44 B=36 and G/B = 44/36 = 11/9