SAT Math has a few word problems that involve ratios, proportions and percentages. Understanding this topic well and being able to apply it to real life problems for in SAT Math will get you well on your way to doing successfully on SAT Math.
What is a ratio?
A ratio is a relationship between the two numbers. Say if you have 5 boys and 6 girls in the class, the ratio between the two genders is 5 to 6. It can be written as
A ratio can be part to part, like the one above, where it’s one part of the whole is related to the other part of the whole.
A ratio can also be part to whole, where one part of the whole is related to the whole or the total amount. So if we relate the number of boys to the total number of students in class, we would have
Ratio Example Problem
A florist picked a bouquet of 7 white roses and 5 red roses.
a) What is the ratio of white roses to red roses?
The ratio of white roses to red roses is 7 to 5.
b) What is the ratio of white roses to total number of roses in the bouquet?
First we need to figure out how many total roses are there in the bouquet by adding the totals for the two types of roses together,
7+5 = 12
Then we can make a ratio of white roses to total number of roses, so the ratio is 7 to 12.
Ratio Practice Problem
Anna plays 1 hour of video games for every 5 hours she studies. What is the ratio of her time spent playing video games to her time spent studying? What is the ratio of her time spent playing video games to the total time she spends playing video games and studying?
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Proportions
When both terms of one ratio can be divided by a constant and end up having the same terms as in the ratio it’s being compared to, the two ratios are proportional. For example,
are proportional because if we divide 10 by 2 and 22 by 2, we get 5/11 or the ratio of 5 to 11. Therefore they are proportional ratios and can be written as
Proportion Example Problem
David eats three times more apples than Bryan. If Bryan ate 5 apples, how many apples did David eat?
First let’s set up the ratio that is given to us up front, which is 1 to 3.
Then let’s equate that ratio to its proportional ratio, so we can find how many apples David ate if Bryan ate 5 apples.
We’ll assign X to the amount of apples that David ate.
Now we solve for X by rearranging the expression.
Multiplying both sides by X and then multiplying them by 3 gives us X=15. So the amount of apples that David ate is 15.
Proportion Practice Problem
Anna plays 1 hour of video games for every 5 hours she studies. If she studied 8 hours, how many hours can she play video games for?
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What is percentage?
Percentage is a proportional ratio of part to whole (total), where the total is always 100.
Percentage Example Problem
In this example if we relate boys in class to total in class using percent, our set of equivalent ratios would be
So to solve for the percent of boys in the class, we rearrange the equation and solve for the missing number. In this case, it is 5/11*100=45 or 45%.
Percentage Practice Problem
Anna plays 1 hour of video games and studies for 5 hours. What percent of the time does she spend playing video games? What percent of the time does she spend studying?
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What is a rate?
A rate is the type of ratio in which the two terms are in different units. For example, 25 miles per hour. The ratio for this rate is 25:1 or 25/1, where 25 is expressed in miles and 1 is expressed in hours.
Rate Example Problem
Tonya travels 50 miles in 1 hour and 15 minutes. What is Tonya’s average speed in miles per hour?
So currently we have a ratio of 50 miles to 1 hour and 15 minutes. We need a ratio of some number of miles per 1 hour of time.
First let’s change 1 hour and 15 minutes to just hours. We need to use a ratio of 60 minutes to 1 hour to do that. So we set up the ratio
Then solve it and we get 0.25 hour, so 15 minutes is 0.25 hour. Now we can solve for the average speed that Tonya traveled in miles per hour.
We take the total miles that she traveled and divide it by the total time she traveled in hours.
Rate Practice Problem
Anna’s iPhone watch said that she burned 350 calories in 1 hour and 30 minutes of walking. What is Ana’s rate of burning calories on hourly basis?
Are you ready to move on to solving SAT Math problems on ratios, proportions and percentages? If so, let’s go to the next article:
SAT Math: Ratios, Proportions, Percentages and Rates Word Problems >
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