The big keyword here is the word RATIO. Ratio of what? The ratio of girls to boys in the entire grade. A ratio is just the two amounts divided by each other (you can also call it the slope, but ignore that if that makes it more confusing).
(81 girls)/(72 boys)
Simplify it by breaking it up a bit.
81 = 9 * 9
72 = 9 * 8
[tex] \frac{9*9}{9*8} [/tex]
Cross out similar terms to gain the result of:
[tex] \frac{9 girls}{8 boys} [/tex]
What they want from us is the ratio of girls if a group has 16 boys. So set it up like this:
[tex] \frac{x girls}{16 boys} = \frac{9 girls}{8 boys} [/tex]
Just by looking at this you may be able to solve for "x" if you have a good understanding of fractions, but instead let's do the long way.
First off is to get "x" alone by multiplying 16 boys on both sides.
x = [tex] \frac{9*16}{8} [/tex]
Remember that:
16 = 8*2
x = [tex] \frac{9*8*2}{8} [/tex]
Cancel out the like terms (8) to give you:
x = 18 girls
