A significant portion of the total digital SAT Math section will be word problems, meaning you'll need to create your own visuals and equations to solve for your answers. Though the actual math topics can vary, SAT word problems share a few commonalities, and we’re here to walk you through how to best solve them.
This post will be your complete guide to SAT Math word problems. We'll cover how to translate word problems into equations and diagrams, the different types of math word problems you’ll see on the test, and how to go about solving your word problems on test day.
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What Are SAT Math Word Problems?
A word problem is any math problem based mostly or entirely on a written description. You will not be provided with an equation, diagram, or graph on a word problem and must instead use your reading skills to translate the words of the question into a workable math problem. Once you do this, you can then solve it.
You will be given word problems on the digital SAT Math section for a variety of reasons. For one, word problems test your reading comprehension and your ability to visualize information.
Secondly, these types of questions allow test makers to ask questions that'd be impossible to ask with just a diagram or an equation. For instance, if a math question asks you to fit as many small objects into a larger one as is possible, it'd be difficult to demonstrate and ask this with only a diagram.
Translating Math Word Problems Into Equations or Drawings
In order to translate your SAT word problems into actionable math equations you can solve, you’ll need to understand and know how to utilize some key math terms. Whenever you see these words, you can translate them into the proper mathematical action.
For instance, the word "sum" means the value when two or more items are added together. So if you need to find the sum of a and b, you’ll need to set up your equation like this: a+b.
Also, note that many mathematical actions have more than one term attached, which can be used interchangeably.
Here is a chart with all the key terms and symbols you should know for SAT Math word problems:
| Key Terms | Mathematical Action |
| Sum, increased by, added to, more than, total of | + |
| Difference, decreased by, less than, subtracted from | − |
| Product, times, __ times as much, __ times as many (a number, e.g., “three times as many”) | * or x |
| Divided by, per, __ as many, __ as much (a fraction, e.g., “one-third as much”) | / or ÷ |
| Equals, is, are, equivalent | = |
| Is less than | < |
| Is greater than | > |
| Is less than or equal to | ≤ |
| Is greater than or equal to | ≥ |
Now, let's look at these math terms in action using a few official examples:
We can solve this problem by translating the information we're given into algebra. We know the individual price of each salad and drink, and the total revenue made from selling 209 salads and drinks combined. So let's write this out in algebraic form.
We'll say that the number of salads sold = S, and the number of drinks sold = D. The problem tells us that 209 salads and drinks have been sold, which we can think of as this:
S + D = 209
Finally, we've been told that a certain number of S and D have been sold and have brought in a total revenue of 836 dollars and 50 cents. We don't know the exact numbers of S and D, but we do know how much each unit costs. Therefore, we can write this equation:
6.50S + 2D = 836.5
We now have two equations with the same variables (S and D). Since we want to know how many salads were sold, we'll need to solve for D so that we can use this information to solve for S. The first equation tells us what S and D equal when added together, but we can rearrange this to tell us what just D equals in terms of S:
S + D = 209
Now, just subtract S from both sides to get what D equals:
D = 209 − S
Finally, plug this expression in for D into our other equation, and then solve for S:
6.50S + 2(209 − S) = 836.5
6.50S + 418 − 2S = 836.5
6.50S − 2S = 418.5
4.5S = 418.5
S = 93
The correct answer choice is (B) 93.
This word problem asks us to solve for one possible solution (it asks for "a possible amount"), so we know right away that there will be multiple correct answers.
Wyatt can husk at least 12 dozen ears of corn and at most 18 dozen ears of corn per hour. If he husks 72 dozen at a rate of 12 dozen an hour, this is equal to 72 / 12 = 6 hours. You could therefore write 6 as your final answer.
If Wyatt husks 72 dozen at a rate of 18 dozen an hour (the highest rate possible he can do), this comes out to 72 / 18 = 4 hours. You could write 4 as your final answer.
Since the minimum time it takes Wyatt is 4 hours and the maximum time is 6 hours, any number from 4 to 6 would be correct.
Though the hardest SAT word problems might look like Latin to you right now, practice and study will soon have you translating them into workable questions.
Typical SAT Word Problems
Word problems on the SAT can be grouped into three major categories:
- Word problems for which you must simply set up an equation
- Word problems for which you must solve for a specific value
- Word problems for which you must define the meaning of a value or variable
Below, we look at each world problem type and give you examples.
Word Problem Type 1: Setting Up an Equation
This is a fairly uncommon type of SAT word problem, but you’ll generally see it at least once on the Math section. You'll also most likely see it first on the section.
For these problems, you must use the information you’re given and then set up the equation. No need to solve for the missing variable—this is as far as you need to go.
Almost always, you’ll see this type of question in the first several questions on the SAT Math section, meaning that the College Board consider these questions easy. This is due to the fact that you only have to provide the setup and not the execution.
It's stated that the vet recommends that, every day, the rabbit eat 25 calories per pound that it weighs, plus an additional 11 calories.
Let's put this in terms of x. If a rabbit weighs x pounds, then multiplying its weight in pounds by 25 calories yields 25x calories.
Adding the additional 11 calories gives us 25x + 11. The question states that c is the total number of calories that the vet recommends a rabbit eat each day.
Put this all together, and you get: c = 25x +11. This means Answer Choice D is the correct answer.
Word Problem Type 2: Solving for a Missing Value
The vast majority of SAT Math word problem questions will fall into this category. For these questions, you must both set up your equation and solve for a specific piece of information.
Most (though not all) word problem questions of this type will be scenarios or stories covering all sorts of SAT Math topics, such as averages, single-variable equations, and ratios. You almost always must have a solid understanding of the math topic in question in order to solve the word problem on the topic.
Let's think about this problem in terms of x. If Scott has 400 employees, randomly selected 20 employees, then found that 16 of those 20 employees are enrolled in 3 professional development courses, then we know that 16/20 employees are in three courses, or 80% because 16/20 is 0.80 or 80/100.
Because the employees were selected randomly, the best way to estimate how many of the 400 total employees are enrolled in exactly three professional development courses this year is to multiply 400 x 0.8. This gives us 320.
Answer Choice B is the correct answer.
You might also get a geometry problem as a word problem, which might or might not be set up with a scenario, too. Geometry questions will be presented as word problems typically because the test makers felt the problem would be too easy to solve had you been given a diagram, or because the problem would be impossible to show with a diagram.
This is a case of a problem that is difficult to show visually, since x is not a set degree value but rather a value greater than 55; thus, it must be presented as a word problem.
Since we know that x must be an integer degree value greater than 55, let us assign it a value. In this case, let us call x 56°. (Why 56? There are other values x could be, but 56 is guaranteed to work since it's the smallest integer larger than 55. Basically, it's a safe bet!)
Now, because x = 56, the next angle in the triangle—2x—must measure the following:
56*2 = 112
Let's make a rough (not to scale) sketch of what we know so far:
Now, we know that there are 180° in a triangle, so we can find the value of y by saying this:
y = 180 − 112 − 56
y = 12
One possible value for y is 12. (Other possible values are 3, 6, and 9.)
Word Problem Type 3: Explaining the Meaning of a Variable or Value
This type of problem will show up at least once. It asks you to define part of an equation provided by the word problem—generally the meaning of a specific variable or number.
Let's break this question down.
The equation y - 5x = 6 represents the relationship between the number of suits that Kaylani made, x, and the total length of fabric that she purchased, y, in yards.
But what does the 6 represent? Let's get one of the variables by itself to see what the equation looks like then. Y is easier to isolate than x, so we'll do that.
Adding 5x to both sides of the equation gives us y = 5x + 6
Because Kaylani made x suits and used 5 yards of fabric to make each suit, 5x represents the total amount of fabric she used to make the suits. Because y represents the total length of fabric Kaylani purchased, then the equation y = 5x + 6 shows us that Kaylani purchased 5x yards of fabric to make the suits, plus an additional 6 yards of fabric.
Therefore, the best interpretation of 6 in this question is that Kaylani purchased
6 yards more fabric than she used to make the suits.
The correct answer is Choice D.
To help juggle all the various SAT word problems, let's look at the math strategies and tips at our disposal.
SAT Math Strategies for Word Problems
Though you’ll see word problems on the SAT Math section on a variety of math topics, there are still a few techniques you can apply to solve word problems as a whole.
#1: Draw It Out
Whether your problem is a geometry problem or an algebra problem, sometimes making a quick sketch of the scene can help you understand what exactly you're working with. For instance, let's look at how a picture can help you solve a word problem about a circle (specifically, a pizza):
If you often have trouble visualizing problems such as these, draw it out. We know that we're dealing with a circle since our focus is a pizza. We also know that the pizza weighs 3 pounds.
Because we'll need to solve the weight of each slice in ounces, let's first convert the total weight of our pizza from pounds into ounces. We're given the conversion (1 pound = 16 ounces), so all we have to do is multiply our 3-pound pizza by 16 to get our answer:
3 * 16 = 48 ounces (for whole pizza)
Now, let's draw a picture. First, the pizza is divided in half (not drawn to scale):
We now have two equal-sized pieces. Let's continue drawing. The problem then says that we divide each half into three equal pieces (again, not drawn to scale):
This gives us a total of six equal-sized pieces. Since we know the total weight of the pizza is 48 ounces, all we have to do is divide by 6 (the number of pieces) to get the weight (in ounces) per piece of pizza:
48 / 6 = 8 ounces per piece
The correct answer choice is (C) 8.
As for geometry problems, remember that you might get a geometry word problem written as a word problem. In this case, make your own drawing of the scene. Even a rough sketch can help you visualize the math problem and keep all your information in order.
#2: Memorize Key Terms
If you’re not used to translating English words and descriptions into mathematical equations, then SAT word problems might be difficult to wrap your head around at first. Look at the chart we gave you above so you can learn how to translate keywords into their math equivalents. This way, you can understand exactly what a problem is asking you to find and how you’re supposed to find it.
There are free SAT Math questions available online, so memorize your terms and then practice on realistic SAT word problems to make sure you’ve got your definitions down and can apply them to the actual test.
#3: Underline and/or Write Out Important Information
Even though the SAT is now digital, you're still allowed scratch paper to take notes and work out problems.
The key to solving a word problem is to bring together all the key pieces of given information and put them in the right places. Make sure you write out all these givens on the diagram you’ve drawn (if the problem calls for a diagram) so that all your moving pieces are in order.
One of the best ways to keep all your pieces straight is to underline your key information in the problem, and then write them out yourself before you set up your equation. So take a moment to perform this step before you zero in on solving the question.
#4: Pay Close Attention to What's Being Asked
It can be infuriating to find yourself solving for the wrong variable or writing in your given values in the wrong places. And yet this is entirely too easy to do when working with math word problems.
Make sure you pay strict attention to exactly what you’re meant to be solving for and exactly what pieces of information go where. Are you looking for the area or the perimeter? The value of x, 2x, or y?
It’s always better to double-check what you’re supposed to find before you start than to realize two minutes down the line that you have to begin solving the problem all over again.
#5: Brush Up on Any Specific Math Topic You Feel Weak In
You're likely to see both a diagram/equation problem and a word problem for almost every SAT Math topic on the test. This is why there are so many different types of word problems and why you’ll need to know the ins and outs of every SAT Math topic in order to be able to solve a word problem about it.
For example, if you don’t know how to find an average given a set of numbers, you certainly won’t know how to solve a word problem that deals with averages!
Understand that solving an SAT Math word problem is a two-step process: it requires you to both understand how word problems work and to understand the math topic in question. If you have any areas of mathematical weakness, now's a good time to brush up on them—or else SAT word problems might be trickier than you were expecting!
All set? Let's go!
Test Your SAT Math Word Problem Knowledge
Finally, it's time to test your word problem know-how against real SAT Math problems:
Word Problems
1.
2.
3.
4.
Answers: A, A, B, A
Aaaaaaaaaaand time for a nap.
Key Takeaways: Making Sense of SAT Math Word Problems
Word problems make up a significant portion of the SAT Math section, so it’s a good idea to understand how they work and how to translate the words on the page into a proper expression or equation. But this is still only half the battle.
Though you won’t know how to solve a word problem if you don’t know what a product is or how to draw a right triangle, you also won’t know how to solve a word problem about ratios if you don’t know how ratios work.
Therefore, be sure to learn not only how to approach math word problems as a whole, but also how to narrow your focus on any SAT Math topics you need help with. You can find links to all of our SAT Math topic guides here to help you in your studies.
What’s Next?
Want to brush up on SAT Math topics? Check out our individual math guides to get an overview of each and every topic on SAT Math. From polygons and slopes to probabilities and sequences, we've got you covered!
Running out of time on the SAT Math section? We have the know-how to help you beat the clock and maximize your score.
Been procrastinating on your SAT studying? Learn how you can overcome your desire to procrastinate and make a well-balanced prep plan.
Trying to get a perfect SAT score? Take a look at our guide to getting a perfect 800 on SAT Math, written by a perfect scorer.
