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fbfe57ec-29be-40e9-a31b-0fd0a58d4b1d.html
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<h4>Cool Down Activity</h4>
<p>On a family outing, Marlon bought 5 cups of hot cocoa and 4 pretzels for $18.40. Some of his family members would like a second serving, so he went back to the same food stand and bought another 2 cups of hot cocoa and 4 pretzels for $11.20.</p>
<p>Here is a system of equations that represent the quantities and constraints in this situation.</p>
<p>\( \left\{ \begin{array}{c l} 5c + 4p = 18.40\\ 2c + 4p = 11.20 \end{array}\right. \)<br>
</p>
<br>
<!--Q#1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="817bf138-e466-46bc-8f10-86871a5e6c6e" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li> What does the solution to the system, \( (c, p) \), represent in this situation?<br>
</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 some samples.</p>
<p>The values of \( c \) and \( p \) represent the price of a cup of hot cocoa and the price of a pretzel that Marlon bought.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="ce348165-65a9-4baa-a08f-ff17aeb96658" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li> If we add the second equation to the first equation, we have a new equation: \( 7c + 8p = 29.60 \). </li>
</ol>
<p>Explain why the same \( (c, p) \) pair that is a solution to the two original equations is also a solution to this new equation.</p>
</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 some samples.</p>
<p>The new equation shows the total number of cups of hot cocoa and total number of pretzels on one side, and the total amount Marlon spent on the other side. The price of each cup of hot cocoa and the price of each pretzel haven’t changed.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="e1105326-bd05-4b3c-bb07-e7590e7516b1" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li> Does the equation \( 7c + 8p = 29.60 \) help us solve the original system? If you think so, explain how it helps. If you don’t think so, explain why not and what would help us solve the system. </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 some samples.</p>
<p>No, it doesn’t help. For example: It doesn’t eliminate a variable. What would help is subtracting the second equation from the first to get
\(3c=7.20\). Then we can find \(c\) and solve for \(p\).</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<h4>Video: Solving Systems of Equations Using Real-World Examples</h4>
<p>Watch the following video to learn more about when addition is useful for solving systems of equations. If you have any questions, play the video again or ask your teacher for clarification.</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><video controls="true" crossorigin="anonymous">
<source src="https://k12.openstax.org/contents/raise/resources/e4e00f7b211b8de51eafad8be8fa2e15f9c49e04">
<track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/af1c3c241d3175f31358f10ec23544a1f4ab1758" srclang="en_us">
https://k12.openstax.org/contents/raise/resources/e4e00f7b211b8de51eafad8be8fa2e15f9c49e04
</video></div>
</div>