-
Notifications
You must be signed in to change notification settings - Fork 1
/
60b5a444-0627-499a-bb84-f1fe4f969f2a.html
91 lines (91 loc) · 5.49 KB
/
60b5a444-0627-499a-bb84-f1fe4f969f2a.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
<h4>Graphing Linear Inequalities in Two Variables to Solve Applications</h4>
<p>Many fields use linear inequalities to model a problem. While our examples may be about simple situations, they give us an opportunity to build our skills and to get a feel for how they might be used.<br>
</p>
<p>For questions 1–3, use the following scenario to write, graph, and find solutions to an inequality:</p>
<p><strong>Example</strong></p>
<blockquote>
<p>Hilaria works two part-time jobs in order to earn enough money to meet her obligations of at least $240 a week. Her job in food service pays $10 an hour and her tutoring job on campus pays $15 an hour. How many hours does Hilaria need to work at each job to earn at least $240? </p>
</blockquote>
<ol class="os-raise-noindent">
<li> Let \(x\) be the number of hours she works at the job in food service and let \(y\) be the number of hours she works tutoring. Write an inequality that would model this situation.</li>
</ol>
<p><strong>Solution:</strong></p>
<p>We let \( x \) be the number of hours she works at the job in food service and let \( y \) be the number of hours she works tutoring. She earns $10 per hour at the job in food service and $15 an hour tutoring. At each job, the number of hours multiplied by the hourly wage will gives the amount earned at that job.</p>
<p><img src="https://k12.openstax.org/contents/raise/resources/cc2b9c88a9651d5c9632e2b4cc49b6aab6b22cfc"></p>
<ol class="os-raise-noindent" start="2">
<li>Graph the inequality. </li>
</ol>
<p>To graph the inequity, we put it in slope-intercept form.</p>
<p>\( \begin{eqnarray} 10x + 15y \geq 240 \\ 15y \geq -10x + 240 \\y \geq - \frac{2}{3}x + 16 \end{eqnarray} \)<br>
</p>
<p><img alt class="img-fluid atto_image_button_text-bottom" height="305" role="presentation" src="https://k12.openstax.org/contents/raise/resources/3ca16ac51454808b8645fea25bfaa8c13d218723" width="300"><br>
</p>
<ol class="os-raise-noindent" start="3">
<li>Find three ordered pairs \((x, y)\) that would be solutions to the inequality. Then, explain what that means for Hilaria.</li>
</ol>
<p>From the graph, we see that the ordered pairs \( (15,10) \), \( (0,16) \), \( (24,0) \) represent three of infinitely many solutions. Check the values in the inequality.</p>
<img alt class="img-fluid atto_image_button_text-bottom" height="161" role="presentation" src=" https://k12.openstax.org/contents/raise/resources/657ed958ce40344d1bbc05587cc508eb290a2c7a" width="675"><br>
<br>
<p>For Hilaria, it means that to earn at least $240, she can work 15 hours tutoring and 10 hours at her fast-food job, earn all her money tutoring for 16 hours, or earn all her money while working 24 hours at the job in food service.</p>
<br>
<h4>Try It: Graphing Linear Inequalities in Two Variables to Solve Applications</h4>
<p>For questions 1–3, use the following scenario to write, graph, and find solutions to an inequality:</p>
<blockquote>
<p>Elijah works two part-time jobs. One is at a grocery store that pays $10 an hour and the other is babysitting for $13 per hour. Between the two jobs, Elijah wants to earn at least $260 a week. How many hours does Elijah need to work at each job to earn at least $260? </p>
</blockquote>
<br>
<!--Q#1-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="4598ea05-f391-419d-b784-55cc817dce9d" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>Let \(x\) be the number of hours he works at the grocery store and let \(y\) be the number of hours he works babysitting. Write an inequality that would model this situation. </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>\(10x+13y \geq 260\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q#2-->
<ol class="os-raise-noindent" start="2">
<li>Graph the inequality. </li>
</ol>
<br>
<div class="os-raise-ib-desmos-gc" 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>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><img src="https://k12.openstax.org/contents/raise/resources/50559651dc86edfbe4480e8f4358916046348fea"></p>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="dfb1f811-1881-47cf-9b4a-8431751e8794" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>Find three ordered pairs \((x, y)\) that would be solutions to the inequality. Then, explain what that means for Elijah. </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.</p>
<p>\((20, 10)\), \((15, 20)\), \((10, 25)\). For each of these coordinate points, if Elijah worked \(x\) hours at the grocery store and \(y\) hours babysitting, he would earn at least $260.</p>
</div>
</div>
<!--Interaction End -->
<br>