# At Central Park Zoo,the ratio of sea lions to penguins is 4 to 11. If there are 84 more penguins than sea lions, how many sea lions are there?

The answer book says: C is the answer. The correct answer should yield a ratio of sea lions to Penguins of 4 to 11, so try out choice C. If there are 48 sea lions, there are 48+84=132 penguins, so the ratio of sea lions to penguins is 48/132=4/11, which is just what we want.

How did they know to pick choice C??

## wait:

132 penguins 4
- = -
48 sea lions 11
i don't think the 2 fractions = eachother(11 doesn't go into 48

## c IS right because 48/132=4/11:

48 divided by 4=12
132 divided by 11=12

## right. Here is they knew to pick those numbers.

Let number sea lions = S
let number penquins = P

We know two things.
S/P = 4/11 AND
S+84=P
Two equations with two unknowns. Solve simultaneously for S and P.
S is 48 and P is 132
and 48/132 is in the ratio of 4/11

## In order to determine which answer choice to pick, the answer book used the given information about the ratio between sea lions and penguins, as well as the fact that there are 84 more penguins than sea lions.

Since the ratio of sea lions to penguins is 4 to 11, the book looked for an answer choice that satisfies this ratio. It's important to note that the ratio of sea lions to penguins should simplify to 4 to 11 when both numbers are divided by their greatest common divisor.

By trying out choice C and assuming there are 48 sea lions, the book calculated that there would be 48 + 84 = 132 penguins. Dividing both numbers by their greatest common divisor, which is 12 in this case, results in a simplified ratio of 4/11, which is the desired ratio.

Therefore, choice C is the correct answer because it satisfies the given ratio of 4 to 11.