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Real-World-Application.html
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<!DOCTYPE html>
<html lang="en">
<head>
<meta name="viewport" content="width=device-width">
<title>Linear Equations Project</title>
<link rel="icon" href="https://tse2.mm.bing.net/th/id/OIP.o4vX1naBWyGzIDpB5FEOFgHaHa?rs=1&pid=ImgDetMain">
<link rel="stylesheet" href="Styles.css">
<div class="topnav">
<a href="index.html">Home</a>
<a href="Challenge.html">Challenge</a>
<a href="Different Methods.html">Finding solutions</a>
<a href="Uses-In-Different-Fields.html">Uses</a>
<a class="active" href="Real-World-Application.html">Real World Problem</a>
<a href="Example.html">Extra Examples</a>
<a href="Final-Puzzle.html">Final Answer</a>
<a href="Graphing-Calculator.html">Desmos Graphing Calculator</a>
</div>
</head>
<body class="body" style= "background-image: url('project.background3.jpg'); background-repeat: no-repeat; background-size: cover;">
<h1 class="text-sizeh2" style="text-align:center;">Real World Application Word Problem</h1>
<h3 class="text-sizeh3" style="text-align:center;" >Starting a Business</h3>
<p class="text-size" style="text-align:center;">
Bill wants to start a 3-D printing business. He figures out that it will cost $250 to get a good 3-D printer that can serve his needs and then an additional $1.4 to make the item. To help him start the business, his parents give him $100. If he sells each item for $11.4, how many items would he have to sell in order to "break even"? Write and solve a system of linear equations that represents this situation.
<br>First, define the variables:
<br>Let the cost in dollars be represented by <em>C</em>
<br>Let the <em><b>in</b></em>come in dollars be represented by <em>I</em>
<br>Let the number of items 3D printed be <em>x</em>
<br>Write the equations:
<br><em>C</em>= 1.4x + 250
<br><em>I</em>= 11.4x + 100
</p>>
<h4 class="text-sizeh4" style="text-align:center;">Solving By Graphing</h4>
<p class="text-size" style="text-align:center;">
<br>Graph these equations:
<br><img src="3D_Printing_Word_Problem.jpg" alt="Graph of Situation" width="900" height="600">
<br>As you can see in this graph, Bill will "break even" when he sells the 15th item.
</p>
<h4 class="text-sizeh4" style="text-align:center;">Solving By Substitution</h4>
<p class="text-size" style="text-align: center;">
In order for Bill to break even, the two equations must equal each other.
<br><em>C</em>=<em>I</em>
<br>1.4x+250=11.4x+100
<br>150=10x
<br>x=15
<br>As you can see, Bill will "break even" when he sells the 15th item.
</p>
<h4 class="text-sizeh4" style="text-align: center;">Solving by elimination</h4>
<p class="text-size" style="text-align: center;">
In order for Bill to break even, the two equations must equal each other.
<br><em>C</em>=<em>I</em>
<br>Use variable <em>y</em> instead of <em>I</em> and <em>C</em> to solve the system.
<br>y = 1.4x + 250
<br>y = 11.4x + 100
<br>Subtract the first equation from the second one to eliminate <em>y</em>.
<br>0=10x-150
<br>150=10x
<br>x=15
<br>As you can see, Bill will "break even" when he sells the 15th item.
</p>
</body>
</html>