<h2>Using a Problem-Solving Strategy For Word Problems</h2>
<p>We have reviewed translating English phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. We have also translated English sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. We restated the situation in one sentence, assigned a variable, and then wrote an equation to solve the problem. This method works as long as the situation is familiar and the math is not too complicated.</p>
<p>Now, we’ll expand our strategy so we can use it to successfully solve any word problem. We’ll list the strategy here, and then we’ll use it to solve some problems. We summarize below an effective strategy for problem solving.</p>
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<h3 data-type="title">Use a Problem-Solving Strategy to Solve Word Problems.</h3>
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<li><strong>Read</strong> the problem. Make sure all the words and ideas are understood.</li>
<li><strong>Identify</strong> what we are looking for.</li>
<li><strong>Name</strong> what we are looking for. Choose a variable to represent that quantity.</li>
<li><strong>Translate</strong> into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebraic equation.</li>
<li><strong>Solve</strong> the equation using good algebra techniques.</li>
<li><strong>Check</strong> the answer in the problem and make sure it makes sense.</li>
<li><strong>Answer</strong> the question with a complete sentence.</li>
</ol>
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<h2>Example</h2>
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<p>Pilar bought a purse on sale for $18, which is one-half of the original price. What was the original price of the purse?</p>
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<h3>Solution</h3>
<p><strong>Step 1. Read</strong> the problem. Read the problem two or more times if necessary. Look up any unfamiliar words in a dictionary or on the internet.</p>
<ul data-bullet-style="bullet">
<li><em>In this problem, is it clear what is being discussed? Is every word familiar?</em></li>
</ul>
<p><strong>Step 2. Identify</strong> what you are looking for. Did you ever go into your bedroom to get something and then forget what you were looking for? It’s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!</p>
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<li><em>In this problem, the words “what was the original price of the purse” tell us what we need to find.</em></li>
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<p><strong>Step 3. Name</strong> what we are looking for. Choose a variable to represent that quantity. We can use any letter for the variable, but choose one that makes it easy to remember what it represents.</p>
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<li>Let $p=$ the original price of the purse.</li>
</ul>
<p><strong>Step 4. Translate</strong> into an equation. It may be helpful to restate the problem in one sentence with all the important information. Translate the English sentence into an algebraic equation.</p>
<p>Reread the problem carefully to see how the given information is related. Often, there is one sentence that gives this information, or it may help to write one sentence with all the important information. Look for clue words to help translate the sentence into algebra. Translate the sentence into an equation.</p>
<table data-label="" summary="We are given the direction to restate the problem in one sentence with all the important information.  To the right of this, we have 18 is one-half the original price. Below this, we are told to translate this into an equation. Hence we have 18 equals 1/2 times p.">
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<td style="width: 494px;">Restate the problem in one sentence with all the important information.</td>
<td style="width: 332px;"><img alt="." src="https://data.ulearngo.com/assets/a8ac6517-9b18-4d37-bc7c-454a2b0fa9c2"/></td>
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<td style="width: 494px;">Translate into an equation.</td>
<td style="width: 332px;"><img alt="." src="https://data.ulearngo.com/assets/69676897-6831-46e9-8173-aba04e284f2b"/></td>
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</tbody>
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<p><strong>Step 5. Solve</strong> the equation using good algebraic techniques. Even if you know the solution right away, using good algebraic techniques here will better prepare you to solve problems that do not have obvious answers.</p>
<table data-label="" style="width: 311px;" summary="We are given the direction to restate the problem in one sentence with all the important information.  To the right of this, we have 18 is one-half the original price. Below this, we are told to translate this into an equation. Hence we have 18 equals 1/2 times p.">
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<td style="width: 178px;">Solve the equation.</td>
<td style="width: 133px;"><img alt="." src="https://data.ulearngo.com/assets/e044a018-3b53-4947-97ee-ad1c878dbc62"/></td>
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<td style="width: 178px;">Multiply both sides by 2.</td>
<td style="width: 133px;"><img alt="." src="https://data.ulearngo.com/assets/f252221c-0287-4b18-9236-c532c6f52e4a"/></td>
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<td style="width: 178px;">Simplify.</td>
<td style="width: 133px;"><img alt="." src="https://data.ulearngo.com/assets/3094e586-4928-49db-8ab7-60773cdd9311"/></td>
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</tbody>
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<p><strong>Step 6. Check</strong> the answer in the problem to make sure it makes sense. We solved the equation and found that $p=36,$ which means “the original price” was $36.</p>
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<li><em>Does $36 make sense in the problem? Yes, because 18 is one-half of 36, and the purse was on sale at half the original price.</em></li>
</ul>
<p><strong>Step 7. Answer</strong> the question with a complete sentence. The problem asked “What was the original price of the purse?”</p>
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<li><em>The answer to the question is: “The original price of the purse was $36.”</em></li>
</ul>
<p>If this were a homework exercise, our work might look like this:</p>
<p>Pilar bought a purse on sale for $18, which is one-half the original price. What was the original price of the purse?</p>
<table data-label="" summary="We are told to let p equal the original price. Below this, we are told 18 is one-half the original price. To the right of this, we have 18 equals 1/2 times p. Below this, we are told to check whether \$36 is a reasonable price for a purse?  The answer is yes. To the right of this, we have 2 times 18 equals 2 times 1/2 times p. Then below this, we have 36 equals p. Below this, we are asked if 18 is one-half of 36. We have 18 equals with a question mark over it 1/2 times 36. Below this, we have 18 equals 18.">
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<td> </td>
<td>Let $p=$ the original price.</td>
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<td> </td>
<td>18 is one-half the original price.</td>
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<td> </td>
<td><img alt="." src="https://data.ulearngo.com/assets/11686f84-79c0-4595-9adb-3437cf13e5c7"/></td>
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<td>Multiply both sides by 2.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/1cd85956-623a-4a27-8874-0f01f6546078"/></td>
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<td>Simplify.</td>
<td><img alt="." src="https://data.ulearngo.com/assets/8bed8eef-2440-4c1e-a0b8-87e39295829a"/></td>
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<td>Check. Is $36 a reasonable price for a purse?</td>
<td> </td>
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<td>Yes.</td>
<td> </td>
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<td>Is 18 one half of 36?</td>
<td> </td>
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<td>$18\stackrel{?}{=}\frac{1}{2}\cdot 36$</td>
<td> </td>
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<td>$18=18✓$</td>
<td> </td>
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<td> </td>
<td>The original price of the purse was $36.</td>
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<p>Let’s try this approach with another example.</p>
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<h2>Example</h2>
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<p>Ginny and her classmates formed a study group. The number of girls in the study group was three more than twice the number of boys. There were 11 girls in the study group. How many boys were in the study group?</p>
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<h3>Solution</h3>
<table data-label="" summary="We are given a table with instructions on the left and mathematical statements on the right. It starts with Step 1. Read the problem. Then we have Step 2. Identify what we are looking for. To the right of this, we have “How many boys did he bring?” Then we have Step 3. Name. Choose a variable to represent the number of boys. To the right of this, we let b equal the number of boys. Then we have Step 4. Translate. Restate the problem in one sentence with all the important information. To the right of this, we have The number of girls (11) was three more than twice the number of boys. Then, translate this into an equation, which gives 11 equals 2b plus 3. Then we have Step 5. Solve the equation. To the right of this, we have 11 equals 2b plus 3. We are told to subtract 3 from each side, so we have 11 minus 3 equals 2b plus 3 minus 3. We are told to simplify, which gives us 8 equals 2b. Then we are told to divide each side by 2, which gives 8/2 equals 2b/2. We are told to simplify, which gives 4 equals b. Then we have Step 6. Check. First, is our answer reasonable? Yes, having 4 boys in a study group seems OK. The problem says the number of girls was three more than twice the number of boys. If there are four boys, does that make eleven girls?  Twice 4 boys is 8. Three more than 8 is 11. Finally, we have Step 7. Answer the question: “There were 4 boys in the study group.”">
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<td style="width: 542px;"><strong>Step 1. Read</strong> the problem.</td>
<td style="width: 396px;"> </td>
</tr>
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<td style="width: 542px;"><strong>Step 2. Identify</strong> what we are looking for.</td>
<td style="width: 396px;">How many boys were in the study group?</td>
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<td style="width: 542px;"><strong>Step 3. Name.</strong> Choose a variable to represent the number of boys.</td>
<td style="width: 396px;">Let $n=$ the number of boys.</td>
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<td style="width: 542px;"><strong>Step 4. Translate.</strong> Restate the problem in one sentence with all the important information.</td>
<td style="width: 396px;"><img alt="." src="https://data.ulearngo.com/assets/9b6c9af6-666e-4d33-9a4c-27eb697158f1"/></td>
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<td style="width: 542px;">Translate into an equation.</td>
<td style="width: 396px;"><img alt="." src="https://data.ulearngo.com/assets/4be8c30c-3af1-4372-ab55-4ab0f715080a"/></td>
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<td style="width: 542px;"><strong>Step 5. Solve</strong> the equation.</td>
<td style="width: 396px;"><img alt="." src="https://data.ulearngo.com/assets/91076d4a-6bbd-4319-a6ba-81ef24538734"/></td>
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<td style="width: 542px;">Subtract 3 from each side.</td>
<td style="width: 396px;"><img alt="." src="https://data.ulearngo.com/assets/c518304d-eafb-48d4-8ece-9a0b78d3af13"/></td>
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<td style="width: 542px;">Simplify.</td>
<td style="width: 396px;"><img alt="." src="https://data.ulearngo.com/assets/d10bb42b-a10d-449e-bfc4-ed2d154279e0"/></td>
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<td style="width: 542px;">Divide each side by 2.</td>
<td style="width: 396px;"><img alt="." src="https://data.ulearngo.com/assets/53ee21c7-05c3-430e-b174-5af6ead37a25"/></td>
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<td style="width: 542px;">Simplify.</td>
<td style="width: 396px;"><img alt="." src="https://data.ulearngo.com/assets/ab7aeb42-da92-4db5-b51a-2ab27b68d036"/></td>
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<td style="width: 542px;"><strong>Step 6. Check.</strong> First, is our answer reasonable? Yes, having 4 boys in a study group seems OK. The problem says the number of girls was 3 more than twice the number of boys. If there are four boys, does that make eleven girls? Twice 4 boys is 8. Three more than 8 is 11.</td>
<td style="width: 396px;"> </td>
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<td style="width: 542px;"><strong>Step 7. Answer</strong> the question.</td>
<td style="width: 396px;">There were 4 boys in the study group.</td>
</tr>
</tbody>
</table>
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Using a Problem-Solving Strategy For Word Problems

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

Mathematics

Discover problem-solving strategies for word problems involving numbers, percentages, and geometry, while also exploring applications of triangles, linear inequalities, and more.


Using a Problem-Solving Strategy For Word Problems

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