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<h4>Activity</h4>
<p>Use the situation you saw earlier to answer questions 1-3.</p>
<blockquote>
<p>Diego bought some raisins and walnuts to make trail mix. Raisins cost $4 a pound and walnuts cost $8 a pound. Diego spent $15 on both ingredients..</p>
</blockquote>
<br>
<!--Q1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="1081d5e8-7ad4-495b-96bd-07e4914a8c3c" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li> Write an equation to represent this constraint. Let \(x\) be the pounds of raisins and \(y\) be the pounds of
walnuts. </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>4x+8y=15.</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q2-->
<ol class="os-raise-noindent" start="2">
<li>Use the graphing tool or technology outside the course. Graph your equation from question 2 that represents this scenario using the Desmos tool below.
</li>
</ol>
<div class="os-raise-ib-desmos-gc" data-bottom="-1" data-top="5" data-left="-1" data-right="5" data-schema-version="1.0"></div>
<br>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
</div>
<div class="os-raise-ib-cta-prompt">
<p>When you have finished graphing, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
<p>Compare your answer:</p>
<img alt="Graph of a line. walnuts (pounds), raisin (pounds)." src="https://k12.openstax.org/contents/raise/resources/d965bc3596a4c65d4f18c5cca702881bf889798c"> <br>
<br>
<br>
</div>
<!--Interaction End -->
<br>
<!--Q3-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal3" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="3">
<li> Complete the table with the amount of one ingredient Diego could have bought given the other. Be prepared to
show your reasoning. </li>
</ol>
<table class="os-raise-midsizetable">
<thead>
<tr>
<th scope="col">Raisins (lbs)</th>
<th scope="col">Walnuts (lbs)</th>
</tr>
</thead>
<tbody>
<tr>
<td>0</td>
<td></td>
</tr>
<tr>
<td>0.25</td>
<td></td>
</tr>
<tr>
<td></td>
<td>1.375</td>
</tr>
<tr>
<td></td>
<td>1.25</td>
</tr>
<tr>
<td>1.75</td>
<td></td>
</tr>
<tr>
<td>3</td>
<td></td>
</tr>
</tbody>
</table>
<br>
</div>
<div class="os-raise-ib-cta-prompt">
<p>When you have filled out the table, select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal3">
<p>Compare your answer:</p>
<table class="os-raise-midsizetable">
<thead>
<tr>
<th scope="col">Raisins (lbs)</th>
<th scope="col">Walnuts (lbs)</th>
</tr>
</thead>
<tbody>
<tr>
<td>0</td>
<td>1.875</td>
</tr>
<tr>
<td>0.25</td>
<td>1.75</td>
</tr>
<tr>
<td>1</td>
<td>1.375</td>
</tr>
<tr>
<td>1.25</td>
<td>1.25</td>
</tr>
<tr>
<td>1.75</td>
<td>1</td>
</tr>
<tr>
<td>3</td>
<td>0.375</td>
</tr>
</tbody>
</table>
<br>
</div>
<!--Interaction End -->
<br>
<p>Use the following new piece of information to answer questions 4 - 6.</p>
<br>
<p>Diego bought a total of 2 pounds of raisins and walnuts combined.</p>
<!--Q4-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="229283b8-1f9c-4ae1-a4a7-6127dc3d59dc" data-fire-event="Reveal4" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li> Write an equation to represent this constraint. Let \(x\) be the pounds of raisins and \(y\) be the pounds of
walnuts. </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal4">
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(x+y=2\)</p>
</div>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q5-->
<ol class="os-raise-noindent" start="5">
<li>Use the graphing tool or technology outside the course. Graph your equation from question 5 that represents this scenario using the Desmos tool below. </li>
</ol>
<div class="os-raise-ib-desmos-gc" data-bottom="-1" data-top="5" data-left="-1" data-right="5" data-schema-version="1.0"></div>
<br>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal5" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
</div>
<div class="os-raise-ib-cta-prompt">
<p>When you have finished graphing, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal5">
<p>Compare your answer:</p>
<img alt="Graph of a line. walnuts (pounds), raisin (pounds)." src="https://k12.openstax.org/contents/raise/resources/a126efd0b1465dbec019f08b2165a251e7afb50d"> <br>
<br>
<br>
</div>
<!--Interaction End -->
<br>
<!--Q6-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal6" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="6">
<li> On your own paper, complete the table with the amount of one ingredient Diego could have bought given the other. Be prepared to
show your reasoning. </li>
</ol>
<table class="os-raise-midsizetable">
<thead>
<tr>
<th scope="col">Raisins (lbs)</th>
<th scope="col">Walnuts (lbs)</th>
</tr>
<tr>
<td>0</td>
<td></td>
</tr>
</thead>
<tbody>
<tr>
<td>0.25</td>
<td></td>
</tr>
<tr>
<td></td>
<td>1.375</td>
</tr>
<tr>
<td></td>
<td>1.25</td>
</tr>
<tr>
<td>1.75</td>
<td></td>
</tr>
<tr>
<td>3</td>
<td></td>
</tr>
</tbody>
</table>
<br>
</div>
<div class="os-raise-ib-cta-prompt">
<p>When you have filled out the table, then select the <strong>solution</strong> button to compare your work.</p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal6">
<p>Compare your answer:</p>
<table class="os-raise-midsizetable">
<thead>
<tr>
<th scope="col">Raisins (lbs)</th>
<th scope="col">Walnuts (lbs)</th>
</tr>
</thead>
<tbody>
<tr>
<td>0</td>
<td>2</td>
</tr>
<tr>
<td>0.25</td>
<td>1.75</td>
</tr>
<tr>
<td>0.625</td>
<td>1.375</td>
</tr>
<tr>
<td>0.75</td>
<td>1.25</td>
</tr>
<tr>
<td>1.75</td>
<td>0.25</td>
</tr>
<tr>
<td>3</td>
<td>-1 (not possible)</td>
</tr>
</tbody>
</table>
<br>
</div>
<!--Interaction End -->
<br>
<p>Use the following information to answer questions 7-9.</p>
<p>Diego spent $15 and bought exactly 2 pounds of raisins and walnuts.</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="80ba97c9-620c-449d-8923-403601b391fd" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q7-->
<div class="os-raise-ib-pset-problem" data-content-id="b05d3cc6-ea6f-494b-8192-510375b2ec87" data-problem-comparator="float" data-problem-type="input" data-solution="0.25">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7">
<li> How many pounds of raisins did he buy? </li>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 0.25</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 0.25. </p>
</div>
</div>
<!--END QUESTION.-->
<!--Q8-->
<div class="os-raise-ib-pset-problem" data-content-id="9f48d8a8-676f-403a-a44b-ed25865eda77" data-problem-comparator="float" data-problem-type="input" data-solution="1.75">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="8">
<li> How many pounds of walnuts did he buy? </li>
</ol>
<p> Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 1.75</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 1.75. </p>
</div>
</div>
<!--END QUESTION.-->
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<br>
<!--Q9-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="70f68e6c-7f38-4c4e-beb9-59ec07c79db1" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="9">
<li> Explain or show how you know how many pounds he purchased of each type. </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Your answer may vary, but here are samples.</p>
<ul>
<li> It’s the only pair of values that appears in both tables. </li>
<li> If the two equations are graphed on the same coordinate plane, it’s where the two graphs intersect, so the pair of values meets both requirements. </li>
</ul>
<img alt="Graph of a linear system. walnuts (pounds), raisin (pounds)." src="https://k12.openstax.org/contents/raise/resources/ae6240fe3890762ae7950155690f4d3f8186d0b9"> <br>
<br>
</div>
</div>
<!--Interaction End -->