Are you ready for SAT Math problems on ratios, proportions, percentages and rates? If you need to review the basics first, check out my previous post for that. Otherwise let’s do some SAT Math example problems.
Example Problem 1
A county repairs 5 miles of public roads every month. How long will it be when 135 miles of road are repaired?
Solution and Explanation
This is a ratio problem, so let’s first find the ratio that is given to us, this ratio is also a rate. It’s 5 miles of roads repaired per 1 month of time.
Next, let’s set up a proportional ratio using 135 miles. It will look like this:
So now, since the ratios are proportional, we will equate them. So we have
Now, let’s solve for x.
First, let’s multiply both sides by x in order to switch x from the denominator to the numerator. We get
Since dividing by 1 gives the same number, we don’t have to write 1 in the denominator of 5x. So we have
Now, we need to isolate x in order to solve for it. So we will divide both sides by 5. So we get
The answer is, it will take 27 months to repair 135 miles of county roads.
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Example Problem 2
Z county’s urban population is 596 people per square mile and it covers 168 square miles. Its suburban population is 67 people per square mile and the suburbs cover 235 square miles. What is the population of Z county in square miles.
Solution steps:
First list what is given to us (sometimes making a table for the data given makes it easier to see and understand the data):
| Type of population | Population / sq mile | Area (sq miles) |
| Urban | 596 | 168 |
| Suburban | 67 | 235 |
Next, understand what needs to be found, or what needs to be solved for – the population of Z county in square miles.
So what the problem is asking for, is the average population of Z county per square mile.
Number one mistake students make is to average the two populations that are already given to us, such as
But this is incorrect, since they don’t take into consideration that the areas of the two types of population are not the same.
Because the areas in square feet of two different areas are not the same, we need to first find out how many total people live in both types of areas and then divide that by the sum of the square mileage that covers both areas.
Setting up the expression:
The answer is 360 people per square mile.
Do you want to see and have me solve more problems like these for your SAT Math or do you need help solving and understanding the above problem?
Are you ready to move on to solving SAT Math problems on ? If so, let’s go to the next article:
SAT Math: Ratios, Proportions, Percentages and Rates Word Problems >
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