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fff9877b-c259-475f-a2d3-95cee4ba4a19.html
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<h4>Activity</h4>
<p>Seniors in a high school student council are trying to develop a budget for the Senior Dance. The revenue from ticket sales needs to cover the cost of the meals and entertainment and also make a profit of at least $200 to be contributed to the school. </p>
<p>Here is some information they have gathered:</p>
<ul>
<li>Last year, 120 people attended. It was a success and is expected to be even bigger this year. Up to 200 people will attend.</li>
<li>There needs to be at least 1 chaperone for every 20 students.</li>
<li>The ticket price cannot exceed $20 per person.</li>
</ul>
<p>Here are some inequalities the seniors wrote about the situation. Each letter stands for one quantity in the situation. Determine what is meant by each letter in questions 1-4.</p>
<br>
<!--Q#1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="b4cc9cc3-5c91-40d5-954a-dcf2918541d9" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>\( t ≤ 20 \)</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>\( t ≤ 20 \) means that the ticket price, \( t \), must be less than or equal to $20.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="a8526120-85df-4e20-9323-85be4187e52b" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>\( 120 ≤ p ≤ 200 \)</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>\( 120 ≤ p ≤ 200 \) means that between 120 and 200 people are expected to attend (120 is less than or equal to the number of people; the number of people is less than or equal to 200). \( p \) represents the number of people attending the dance.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="64539d39-214b-4cbf-baf7-21a9e0e5ef70" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>\( pt - m ≥ 200 \)</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>\( pt − m ≥ 200 \) means that the total amount collected from ticket sales in dollars, \( pt \), minus the cost of meals and entertainment in dollars, \( m \), must be greater than or equal to $200.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#4-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="bd9d4eaf-4661-4a44-8b07-1dc4fd8a4017" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>\( c \geq \frac{p}{20} \)</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>\( c \geq \frac{p}{20} \) means that the number of chaperones, \( c \), must be at least \( \frac{1}{20} \) of the number of students attending.</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!-- "Start "Are you Ready for More? click to reveal. If you have more than one on a page, you will need to change the Data-fire/data-wait-for-events for each set.-->
<div class="os-raise-ib-cta" data-button-text="Are you ready for more?" data-fire-event="RFM1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-cta-prompt">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="66c5c0dc-1a48-40a8-9457-8d89c874c623" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<h4>Extending Your Thinking</h4>
<p>Kiran says we should add the constraint \( t ≥ 0 \).</p>
<ol class="os-raise-noindent">
<li>What is the reasoning behind this constraint?</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>We can't have a negative ticket price.</p>
</div>
</div>
<!--End interaction-->
<br>
<!--Q#2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="a78479ec-7b7f-4cb5-8b94-b0e67b46f3be" data-schema-version="1.0" data-wait-for-event="RFM1">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>What other “natural constraint” like this should be added?</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>By the same reasoning, we might want to include \(m \geq 0\). Note that the other variables should also be greater than or equal to 0, but those conditions are already implied by the existing constraints.</p>
</div>
</div>
<!--End interaction-->
<br>