# Ratios

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## 4/27 Ratios

Always remember to follow the Knowsys Math Method. This may take longer than simply solving the problem at first, as you learn the method, but it will save you time once you begin to use it consistently. Reading carefully will help you make sure you don't miss anything. Identifying the bottom line makes it clear exactly what you are looking for. Stopping to assess your options will help you select the most efficient way to solve every problem and keep you from losing time by spending too much time on a problem. Finally, looping back will ensure that the answer you found matches the question that was asked; if you found the value of m, but the question asked for m + 3, you might get that problem wrong even after doing all the math correctly.

A jar contains only red marbles and green marbles. If a marble is selected at random from the jar, the probability that a red marble will be selected is $\frac{2}{3}$. If there are 36 green marbles in the jar, how many red marbles are in the jar?

When reading carefully, take note of facts that could help you solve the problem. For example, the fact that the jar only has red and green marbles means that this problem will involve only two variables, probably r and g. Later, the value of g is given, and the problem asks how many red marbles there are. The marbles are selected at random; that's good because it means you can rely on the probability given. If you reached into the jar looking for a red marble, the odds of finding one would be extremely high, no matter what the ratio of red marbles to green marbles is.

Next, identify the bottom line. The question asks "how many red marbles are in the jar?" That can be summarized as

r = ?

Now, assess your options. You could try plugging in the answers until you find one that works, but that could take a while. Or you could try setting up a proportion with the red and green marbles to calculate the number of red marbles in the jar. Conveniently, a ratio is already provided! You're halfway done already! So if there are two red marbles for every... Oh wait.

This is an example of why reading carefully is important. The ratio you need to find to solve the problem is r:g, but the ratio the problem gives you is r:a, or the ratio or red marbles to all the marbles in the jar. So, if 2 out of every 3 marbles are red, the remaining 1 must be green. Now you can set up a proportion.

$\frac{red}{green}=\frac{2}{1}=\frac{x}{36}$

It is essential that you always label your scratch work so that it is clear not just what you are doing, but what you did. When you reach the end of a section and begin to work backwards, double-checking problems you're not sure about, labels are invaluable because they show what you did to solve the problem. Now that the proportion is set up, you can solve it easily.

$36(\frac{2}{1})=36(\frac{x}{36})$

36(2) = x

x = 72

Now look at the answer choices:

A) 18

B) 24

C) 54

D) 72

E) 108