How To Help Students With Money Word Problems

About 25% of your total Sabbatum Math division will equal word problems, significant you leave have to make up your own visuals and equations to solve for your answers. Though the real math topics can vary, Sat word problems share a few commonalities, and we're Here to walk you through how to incomparable solve them.

This send will be your complete guide to SAT Math word problems. We'll overcompensate how to translate word of honor problems into equations and diagrams, the different types of math word problems you'll see on the test, and how to go astir solving your word problems on test day.

Feature Image: Antonio Litterio/Wikimedia

What Are SAT Math Word Problems?

A word problem is any math trouble based mostly or entirely on a written description. You volition not be furnished 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 possible math job. Once you do this, you can so solve it.

You will incline Logos problems on the SAT Math section for a kind 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 unsurmountable to ask in with just a plot or an equation. For instance, if a math question asks you to fit as many small objects into a bigger one as is possible, IT'd be difficult to demonstrate and call for this with only a diagram.

Translating Maths Word Problems Into Equations operating room Drawings

In order to translate your SAT password problems into actionable math equations you can solve, you'll need to translate and know how to use some key math damage. Whenever you see these words, you can translate them into the suited mathematical action.

For instance, the word "sum" means the value when two Beaver State more items are added collectively. So if you need to find the sum of a and b, you'll need to set up your equation the likes of this: a+b.

Also, note that many mathematical actions have more one terminal figure attached, which can follow used interchangeably.

Here is a graph with all the important terms and symbols you should know for SAT Maths word problems:

Keystone Terms	Mathematical Action
Total, increased by, added to, more than, total of	+
Difference, decreased by, to a lesser degree, subtracted from	−
Product, times, __ multiplication As much, __ multiplication as many (a number, e.g., "three times as more")	* or x
Divided away, per, __ as many another, __ as much (a fraction, e.g., "third As much")	/ OR ÷
Equals, is, are, equivalent	=
Is less than	<
Is greater than	>
Is to a lesser degree or equal to	≤
Is greater than or equal to	≥

Instantly, countenance's consider these maths damage in action victimization few official examples:

We can solve this problem by translating the selective information we're given into algebra. We have it off the individual price of all salad and drink, and the total revenue made from marketing 209 salads and drinks combined. So let's write this call at 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 remember every bit this:

S + D = 209

At last, 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 direct numbers of S and D, but we do know how very 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 an salads were sold, we'll need to solve for D sol 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 price of S:

S + D = 209

Right away, just take off S from both sides to get what D equals:

D = 209 − S

In conclusion, wa this expression certain D into our other equation, and and so 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 precise resolution choice is (B) 93.

This news trouble asks America to solve for one possible solution (it asks for "a possible amount"), so we acknowledge immediately that there will be multiple rectify answers.

James Wyatt tail end husk leastwise 12 cardinal ears of corn and at most 18 dozen ears of corn per hour. If he husks 72 twelve at a rate of 12 twelve 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 clip is 6 hours, any number from 4 to 6 would be correct.

Though the hardest SAT word problems might look like Latin to you accurate straight off, practice and study will presently have you translating them into executable questions.

Typical SAT Word Problems

Word problems on the SAT hind end be grouped into triplet major categories:

• Word problems for which you must simply set up an equality
• Word problems for which you must solve for a specific value
• Word problems for which you must define the meaning of a rate or variable

Below, we look at each world problem type and give you examples.

Word Trouble Type 1: Setting Up an Equivalence

This is a fairly uncommon character of SAT word of honor problem, but you'll generally see IT at least once on the Mathematics section. You'll also most likely understand IT first on the division.

For these problems, you must use the info you're given and then hardening up the par. No need to solve for the wanting variable—this is Eastern Samoa far as you need to go.

Just about always, you'll see this type of question in the eldest four questions on the SAT Math section, meaning that the College Board consider these questions easy. This is collect to the fact that you only cause to provide the setup and not the carrying into action.

To solve this problem, we'll need to know both Armand's and Tyrone's situations, thus let's front at them separately:

Armand: Armand sent m text messages each minute for 5 hours, and then we can write out this as 5m—the number of texts he dispatched per hour multiplied by the total number of hours he texted.

Tyrone: Tyrone transmitted p text messages each hour for 4 hours, so we can pen this as 4p—the number of texts he sent per hour multiplied away the total number of hours he texted.

We now know that Armand's situation can be written algebraically as 5m, and Tyrone's can be written as 4p. Since we're organism asked for the expression that represents the total amoun of texts sent by Armand and Tyrone, we must add together the deuce expressions:

5m + 4p

The correct answer is choice (C) 5m + 4p

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 specify up your equation and solve for a specialized art object of info.

Most (though not all) word problem questions of this type will be scenarios operating theater stories covering all sorts of SAT Math topics, such as averages, single-variable equations, and ratios. You most always must have a jelled discernment of the math subject doubtful in order to solve the intelligence problem happening the topic.

Allow's try to toy with this problem in terms of x. If Case A trees produced 20% Thomas More pears than Case B did, we can write this as an facial expression:

x + 0.2x = 1.2x = # of pears produced by Type A

In this equation, x is the numerate of pears produced away Type B trees. If we add 20% of x (0.2x) to x, we get the number of pears produced by Case A trees.

The problem tells America that Character A trees produced a total of 144 pears. Since we know that 1.2x is balanced to the number of pears produced past Typecast A, we buns write the following equation:

1.2x = 144

Now, all we have to do is part both sides by 1.2 to line up the number of pears produced aside Type B trees:

x = 144 / 1.2

x = 120

The correct answer choice is (B) 120.

You might also get a geometry trouble as a Son problem, which mightiness or power non represent set up with a scenario, too. Geometry questions will be conferred as word problems typically because the test makers felt the problem would be too easy to solve had you been given a plot, or because the problem would be impossible to show with a diagram. (Note that geometry makes up a selfsame small percentage of SAT Math.)

This is a case of a problem that is difficult to show visually, since x is not a set degree value only rather a value greater than 55; thus, it must be presented every bit 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 United States of America call x 56°. (Wherefore 56? There are different values x could personify, only 56 is guaranteed to work since IT's the smallest integer larger than 55. Basically, it's a uninjured stake!)

Now, because x = 56, the next angle in the triangle—2x—must measure the followers:

56*2 = 112

Let's make a rough (non to scale) sketch of what we know thus far:

Now, we know that there are 180° in a triangle, so we can find the value of y away saying this:

y = 180 − 112 − 56

y = 12

One possible value for y is 12. (Other realistic values are 3, 6, and 9.)

Word Trouble Type 3: Explaining the Meaning of a Variable or Value

This type of job will show up at any rate erstwhile. It asks you to define divide of an equation provided by the word problem—generally the significant of a specific variable or number.

This interrogate might sound tricky at first, but information technology's actually quite dewy-eyed.

We know that P is the number of phones Kathy has left to fix, and d is the number of days she has worked in a week. If she's worked 0 days (i.e., if we plug 0 into the equation), here's what we get:

P = 108 − 23(0)

P = 108

This means that, without working whatsoever years of the week, Kathy has 108 phones to vivify. The objurgate suffice selection, therefore, is (B) Kathy starts each week with 108 phones to get.

To help juggle all the various SAT word problems, let's look at the maths strategies and tips at our disposal.

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SAT Mathematics Strategies for Word Problems

Though you'll see word problems happening the SAT Math section on a potpourri of math topics, in that respect are still a couple of techniques you can utilise to solve word problems as a whole.

#1: Draw It Out

Whether your trouble is a geometry trouble or an algebra problem, sometimes making a quick outline of the shot can help you understand what exactly you'Re temporary with. For representativ, let's look at how a picture can help you solve a word problem about a circle (specifically, a pizza):

If you often hold trouble visualizing problems such as these, draw IT come out. We know that we're transaction with a circle since our focus is a pizza. We also know that the pizza pie weighs 3 pounds.

Because we'll need to solve the angle of each slice in ounces, LET's first convert the total weight down of our pizza from pounds into ounces. We'rhenium tending the conversion (1 quid = 16 ounces), so all we have to do is multiply our 3-pound pizza by 16 to get our resolve:

3 * 16 = 48 ounces (for whole pizza pie)

Now, allow's draw a picture. Eldest, the pizza pie is divided in half (not drawn to scale):

We now have two equal-shrew-sized pieces. Rent's continue drawing. The problem then says that we divide each uncomplete into three equal pieces (again, not drawn to weighing machine):

This gives us a entire of six equal-sized pieces. Since we bon the total weight of the pizza is 48 ounces, completely we have to do is divide by 6 (the phone number of pieces) to get the weight (in ounces) per piece of pizza:

48 / 6 = 8 ounces per piece

The correct resolution choice is (C) 8.

As for geometry problems, remember that you might get a geometry word problem scripted as a word problem. In this case, make your own drawing off of the scene. Even a cragged cartoon can help you visualize the math trouble and keep completely your information in order.

#2: Memorize Paint Terms

If you're not used to translating English words and descriptions into exact equations, and so Sat word problems might be difficult to wrap your head around at 1st. Facial expression at the chart we gave you preceding thus you give the sack learn how to translate keywords into their math equivalents. This way, you can realise exactly what a trouble is asking you to detect and how you'Re supposed to find it.

There are on the loose SAT Math questions purchasable online, so memorise your terms and then practice on realistic Sat word problems to make sure you've got your definitions down and rear apply them to the actual test.

#3: Underscore and/or Write Out Of the essence Information

The key to solving a word problem is to convey together all the key pieces of apt information and put them in the right field places. Score sure enough you write out all these givens on the plot you've drawn (if the trouble calls for a diagram) so that all your moving pieces are in order.

One of the best ways to proceed totally your pieces straight is to underscore your key information in the job, so spell them out yourself in front you lay out your equation. So make a second to do this step before you home in on solving the question.

#4: Pay off Close Attention to What's Being Asked

It can be infuriating to find yourself solving for the wrong inconstant or writing in your donated values in the wrong places. And withal this is entirely too easy to do when impermanent with math word problems.

Make sure you pay strict attention to exactly what you're meant to be solving for and on the dot what pieces of entropy go where. Are you looking for the area or the circumference? The evaluate of x, 2x, operating room y?

Information technology's ever punter to dual-check what you're theoretic to find before you start than to realize deuce minutes John L. H. Down the product line that you have to begin solving the job everywhere again.

#5: Brush Up on Any Specific Math Issue You Feel Weak In

You'Ra likely to realize both a plot/equality problem and a word problem for almost every SAT Maths matter 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 Mathematics topic in order to comprise able to solve a formulate problem about it.

For example, if you father't know how to chance 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 Mathematics Book trouble is a two-stride work on: it requires you to both understand how phrase problems work and to understand the math topic in call into question. If you sustain whatever areas of mathematical weakness, now's a good meter to brush informed them—or else SAT password problems might be trickier than you were expecting!

Whol set? Let's spell!

Test Your SAT Math Word Trouble Cognition

Finally, it's time to test your Book trouble know-how against factual SAT Math problems:

Word Problems

1. No Estimator

2. Calculator OK

3. Reckoner Sooner State

4. Calculator OK

Answers: C, B, A, 1160

Answer Explanations

1. For this trouble, we have to manipulation the information we're given to effectuate an equation.

We know that Ken spent x dollars, and Paul spent 1 one dollar bill more than Ken did. Therefore, we can write the following equation for Paul:

x + 1

Ken and Paul split the handbill evenly. This means that we'll have to solve for the total amount of some their sandwiches and past divide it by 2. Since Cognizance's sandwich toll x dollars and Paul's cost x + 1, here's what our equation looks like when we combine the two expressions:

x + x + 1

2x + 1

Now, we can divide this expression by 2 to get the price each somebody freelance:

(2x + 1) / 2

x + 0.5

But we'ray not finished thus far. We know that both Ken and Paul also paid a 20% baksheesh on their bills. As a result, we own to multiply the tot up monetary value of one bill by 0.2, and then add up this lean on to the bill. Algebraically, this looks like this:

(x + 0.5) + 0.2(x + 0.5)

x + 0.5 + 0.2x + 0.1

1.2x + 0.6

The counterbalance reply choice is (C) 1.2x + 0.6

2. You'll have to be acquainted statistics in order to understand what this question is asking.

Since Dent surveyed a ergodic taste of his freshman class, we can articulate that this sample bequeath accurately reverberate the opinion (and thus the same percentages) as the whole freshman class.

Of the 90 freshmen sampled, 25.6% said that they wanted the Split up Festival held in October. Entirely we bear to do directly is find this percentage of the entire freshmen class (which consists of 225 students) to determine how many total freshmen would prefer an October fete:

225 * 0.256 = 57.6

Since the interrogative sentence is asking "or so how umpteen students"—and since we obviously can't have a fraction of a mortal!—we'll have to encircle this number to the nighest answer select addressable, which is 60, or answer choice (B).

3. This is single of those problems that is interrogatory you to define a treasure in the equation presumption. It might look confusing, but father't be scared—information technology's actually not as difficult as information technology appears!

Prototypic off, we know that t represents the number of seconds passed after an object is launched upward. But what if no time has passed yet? This would mean that t = 0. Here's what happens to the equation when we plug in 0 for t:

h(0) = -16(0)2 + 110(0) + 72

h(0) = 0 + 0 + 72

h(0) = 72

As we keister see, before the object is even launched, it has a height of 72 feet. This substance that 72 must represent the first height, in feet, of the object, OR answer choice (A).

4. You might beryllium tempted to absorb a diagram for this problem since it's talking about a pool (rectangle), only it's really quicker to just look at the Book of Numbers given and employment from thither.

We know that the pool currently holds 600 gallons of water and that water has been hosed into it at a charge per unit of 8 gallons a bit for a total of 70 minutes.

To witness the amount of water in the pool now, we'll have to first solve for the add up of water added to the pool aside hose. We know that 8 gallons were added each minute for 70 minutes, indeed totally we have to do is multiply 8 by 70:

8 * 70 = 560 gallons

This tells us that 560 gallons of water were added to our already-filled, 600-gallon pool. To ascertain the total amount of body of water, then, we simply add these two numbers together:

560 + 600 = 1160

The correct result is 1160.

Aaaaaaaaaaand time for a nap.

Primal Takeaways: Making Mother wit of SAT Math Word Problems

Word problems make upwards a significant portion of the SAT Maths section, so it's a good mind to understand how they work and how to translate the dustup on the page into a proper expression or par. But this is still sole fractional the battle.

Though you won't know how to solve a word trouble if you don't acknowledge what a product is or how to draw a right triangle, you also won't know how to wor a word job or so ratios if you don't know how ratios work.

Therefore, personify sure to learn non only how to approach math formulate problems as a integral, but also how to narrow your concentrate on any SAT Math topics you need help with. You can breakthrough links to all of our SAT Math theme guides Here to serve you in your studies.

What's Succeeding?

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About the Author

Courtney scored in the 99th centile on the Sat in high schooltime and went happening to graduate from Stanford University with a degree in Cultural and Social Anthropology. She is passionate about bringing education and the tools to succeed to students from all backgrounds and walks of life, American Samoa she believes open educational activity is one of the great societal equalizers. She has long time of tutoring experience and writes fanciful works in her free prison term.

How To Help Students With Money Word Problems

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