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333e27e0-9279-4ae1-a41a-991b4b245a39.html
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<h4>Activity</h4>
<p>Use this information to answer questions 1 and 2.</p>
<blockquote>
<p>To help pay for his tuition, a college student plans to work in the evenings and on weekends. He has been offered two part-time jobs: working in the guest-services department at a hotel and waiting tables at a popular restaurant.</p>
<ul>
<li>The job at the hotel pays <span>$</span>18 an hour and offers $33 in transportation allowance per month.</li>
<li>The job at the restaurant pays <span>$</span>7.50 an hour plus tips. The entire wait staff typically collects about $50 in tips each hour. Tips are divided equally among the 4 wait staff members who share a shift.</li>
</ul>
<p>The equation \( 7.50h + \frac {50}{4}h = 18h + 33 \) represents a possible constraint about a situation for 1 month.</p>
<br>
</blockquote>
<!--Text Entry Interaction Start -->
<!--Q #1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="2c227ada-05e7-4808-a509-7c13134b71f2" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>Solve the equation and check your solution.</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: \( h=16.5 \)</p>
<p>\( 7.50h + \frac {50}{4}h = 18h + 33 \)</p>
<p>\( 7.50(16.5) + \frac {50}{4}(16.5) = 18(16.5) + 33 \)</p>
<p>\(123.75+206.25=297+33\)</p>
<p>\(330=330 \checkmark\)</p>
</div>
</div>
<!--Interaction End -->
<!-- BEGIN CLICK TO REVEAL NO TEXTBOX -->
<br>
<!--Q#2-->
<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">
<ol class="os-raise-noindent" start="2">
<li>Add a scale on the number line so that the point marked with a circle represents the solution to the equation you found in question 1.<br>
<img alt="A blank number line is shown with an open circle on a point in the middle.
" height="16" src="https://k12.openstax.org/contents/raise/resources/3ab9d6c1efc50cac2d8c8e66fde938a8366ee2ea" width="359"><br>
</li>
</ol>
</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>
<p>Your answer may vary, but here is a sample.</p>
<img alt=" A number line is shown from 14 to 19 with an
open circle on 16.5.
" height="49" role="presentation" src="https://k12.openstax.org/contents/raise/resources/cbb591ba5a80826249f1873eaae5aa3e06798849" width="400">
</div>
<!--Interaction End -->
<br>
<!-- END CLICK TO REVEAL NO TEXTBOX -->
<!-- BEGIN ACTIVITY DROP DOWN 1 TRY -->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="c39b03e0-2e67-4e63-a9cd-703df54a0d5d" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q#3-->
<div class="os-raise-ib-pset-problem" data-content-id="29538925-54ad-4d51-8b1a-d3614dd56a74" data-problem-type="dropdown" data-solution="Hotel Job" data-solution-options='["Hotel Job", "Restaurant Job","The pay is the same."]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3">
<li>Which job pays better if he works fewer hours than the solution you found in question 1? </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Hotel Job.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is the hotel job.</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>
<!--END ACTIVITY DROP DOWN 1 TRY -->
<br>
<!--Text Entry Interaction Start -->
<!--Q #4-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="dbcd9b81-b203-45fe-b679-caf28676e98f" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>Explain how you know.</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 is a sample. The hotel job pays better if he works fewer than 16.5 hours a month because I found the pay for both jobs using numbers that are less than 16.5 and found that pay at the hotel job is always higher.</p>
</div>
</div>
<!--Interaction End -->
<br>
<!-- BEGIN ACTIVITY DROP DOWN 1 TRY -->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="a238e16b-802f-4267-b930-4c66a5e9f015" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q#5-->
<div class="os-raise-ib-pset-problem" data-content-id="7105cfee-99ee-4db0-9d8f-4882349ffbd7" data-problem-type="dropdown" data-solution="Restaurant Job" data-solution-options='["Hotel Job", "Restaurant Job","The pay is the same."]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li>Which job pays better if he works more hours than the solution you found in question 1? </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Restaurant Job.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is the restaurant job.</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>
<!--END ACTIVITY DROP DOWN 1 TRY -->
<br>
<!--Text Entry Interaction Start -->
<!--Q #6-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="b540b6c5-f02d-4058-ade0-3581d980da27" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="6">
<li>Explain how you know.</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 is a sample. The restaurant job pays better if he works more than 16.5 hours a month because I found the pay for both jobs using numbers that are more than 16.5 and found that pay at the restaurant job is always higher.</p>
</div>
</div>
<!--Interaction End -->
<br>
<!-- BEGIN CLICK TO REVEAL NO TEXTBOX -->
<br>
<!--Q#7-->
<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">
<ol class="os-raise-noindent" start="7">
<li>Draw a number line, including a scale, so that the point marked with a circle represents the solution to the inequality: \( 7.50h + \frac {50}{4}h < 18h + 33 \).<br>
<img alt="A blank number line is shown with an open circle on a point in the middle.
" height="16" src="https://k12.openstax.org/contents/raise/resources/3ab9d6c1efc50cac2d8c8e66fde938a8366ee2ea" width="359"><br>
</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, 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>
<p>Your answer may vary, but here is a sample.</p>
<img alt="A number line is shown with an open circle on a point in the middle. The number is shaded to the left of the open circle." role="presentation" src="https://k12.openstax.org/contents/raise/resources/a327c5c2188e135b8663490def2e46453251b269" width="400">
</div>
<!--Interaction End -->
<br>
<!-- END CLICK TO REVEAL NO TEXTBOX -->
<!-- BEGIN CLICK TO REVEAL NO TEXTBOX -->
<br>
<!--Q#8-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal2" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="8">
<li>Draw a number line, including a scale, so that the point marked with a circle represents the solution to the inequality: \( 7.50h + \frac {50}{4}h > 18h + 33 \).<br>
<img alt="A blank number line is shown with an open circle on a point in the middle.
" height="16" src="https://k12.openstax.org/contents/raise/resources/3ab9d6c1efc50cac2d8c8e66fde938a8366ee2ea" width="359"><br>
</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, 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="Reveal2">
<p>Compare your answer:</p>
<p>Your answer may vary, but here is a sample.</p>
<img alt="A number line is shown with an open circle on a point in the middle. The number is shaded to the right of the open circle." role="presentation" src="https://k12.openstax.org/contents/raise/resources/8466273512a48d78a5d5e98d3a991cd06a57e2cb" width="400"><br>
</div>
<!--Interaction End -->
<br>
<!-- END CLICK TO REVEAL NO TEXTBOX -->
<!-- BEGIN TEXT ENTRY WITH REVEAL -->
<br>
<!--Q#9-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="00b03237-54dc-4403-a6b7-139ee2d20680" 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 how you know. </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>
<ul>
<li>Inequality 1 shows the pay at the hotel \( (18h+33) \) being greater than the pay at the restaurant \( 7.50h+ \frac{50}{4} \). Earlier, we found out that the hotel job is better when the student works less than 16.5 hours. Graph B shows \( h<16.5 \). This means Graph B shows the solution to Inequality 1.</li>
<li>If we substitute a value greater than 16.5 for \( h \), we have a true statement for Inequality 2 and a false statement for Inequality 1. This means \( h>16.5 \) is a solution to Inequality 2 but not to Inequality 1. </li>
<li>If we substitute a value less than 16.5 for \( h \), we have a true statement for Inequality 1 but not for Inequality 2. So \( h<16.5 \) is a solution to Inequality 1.</li>
</ul>
</div>
</div>
<!--Interaction End -->
<br>
<!-- END TEXT ENTRY WITH REVEAL -->