Solving Proportions Word Problems - Examples & Practice

Proportions in Word Problems

The first step in solving any word problem is translating it from words to mathematical expressions.

Let's start by writing a fraction to represent the ratio of mammals to reptiles in the zoo.

The information in the problem can be translated into a proportion like this:

I'm going to solve the proportion using cross-multiplication, but you can also use more traditional multiplication. Pick whichever method is most comfortable for you.

It's always a good idea to double check your answer!

Let's try another example.

We need to set up a proportion to solve this problem.

Remember to double check your answer!

Proportion Word Problem Walk-through

We're going to walk through a word problem dealing with proportions!

Mark Trumbo of the Arizona Diamondbacks has hit five home runs in the thirty-five times he has been up to bat. At this pace, how many at bats would he need to hit twenty-three home runs?

We want to set up a ratio here. Let's choose: $$\text{Home Runs(HR)}:\text{At Bats(AB)}$$ So our proportion will be in the form: $$\frac{\text{HR}}{\text{AB}}=\frac{\text{HR}}{\text{AB}}$$ The first bit of information is that he hit five home runs in the thirty-five times he has been up to bat. Therefore, the first ratio of our proportion will be $$\frac5{35}=\frac{\text{HR}}{\text{AB}}$$ For our second proportion we want to know how many at bats would he need to hit twenty-three home runs. The home runs are $23$ and the at bats are unknown. $$\frac5{35}=\frac{23}x$$ From here we can just take the cross product and solve.

Remember to simplify your fractions!

Finally, we state our answer. $$\begin{gather} \text{He would need to be at bat }161\text{ times}\\ \text{to hit }23\text{ home runs.} \end{gather}$$

Rate Word Problems

To solve this word problem, we need to figure out how many words Kayla can type per minute.

The word per is a trigger, telling you that we are going to be working with ratios and rates.

We can use this same method to solve rates that deal with time and distance!