Permalink
Fetching contributors…
Cannot retrieve contributors at this time
127 lines (120 sloc) 6.49 KB
<!DOCTYPE html>
<html data-require="math math-format word-problems">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Writing proportions</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<div class="problems">
<div id="original" data-weight="1">
<div class="vars">
<var id="N1">randRange( 2, 10 )</var>
<var id="N2">randRangeExclude( 2, 15, [ N1 ] )</var>
<var id="C">localeToFixed( N1 * randRange( 80, 199 ) / 100, 2)</var>
<var id="SOLUTION">"\\dfrac{" + N1 + "}{\\$" + C + "} = \\dfrac{" + N2 + "}{x}"</var>
</div>
<p class="problem">
<code><var>N1</var></code> <var>plural_form(deskItem(0), N1)</var> cost <code>\$<var>C</var></code>.
</p>
<p class="question">
Which equation would help determine the cost of <code><var>N2</var></code> <var>plural_form(deskItem(0), N2)</var>?
</p>
<p class="solution"><code><var>SOLUTION</var></code></p>
<ul class="choices" data-none="true" data-show="5">
<li><code>\dfrac{<var>N2</var>}{\$<var>C</var>} = \dfrac{x}{<var>N1</var>}</code></li>
<li><code>\dfrac{<var>N2</var>}{<var>N1</var>} = \dfrac{\$<var>C</var>}{x}</code></li>
<li><code>\dfrac{<var>N1</var>}{<var>N2</var>} = \dfrac{x}{\$<var>C</var>}</code></li>
<li><code>\dfrac{x}{<var>N2</var>} = \dfrac{<var>N1</var>}{\$<var>C</var>}</code></li>
<li><code>\dfrac{<var>N2</var>}{x} = \dfrac{\$<var>C</var>}{<var>N1</var>}</code></li>
</ul>
<div class="hints">
<p>
We can write the fact that <code><var>N1</var></code>
<var>plural_form(deskItem(0), N1)</var> cost <code>\$<var>C</var></code> as a proportion:
</p>
<p><code>\qquad \dfrac{<var>N1</var>}{\$<var>C</var>}</code></p>
<p>
Let <code>x</code> represent the unknown cost of <code><var>N2</var></code> <var>plural_form(deskItem(0), N2)</var>.
Since <code><var>N2</var></code> <var>plural_form(deskItem(0), N2)</var> cost <code>x</code>,
we have the following proportion:
</p>
<p><code>\qquad \dfrac{<var>N2</var>}{x}</code></p>
<p>
The cost changes along with the number of <var>plural_form(deskItem(0))</var> purchased,
and so the two proportions are equivalent.
</p>
<p><code>\qquad <var>SOLUTION</var></code></p>
</div>
</div>
<div data-type="original" data-weight="1">
<div class="vars">
<var id="SOLUTION">"\\dfrac{" + N2 + "}{x} = \\dfrac{" + N1 + "}{\\$" + C + "}"</var>
</div>
<div class="hints">
<p>
Let <code>x</code> represent the unknown cost of <code><var>N2</var></code> <var>plural_form(deskItem(0), N2)</var>.
Since <code><var>N2</var></code> <var>plural_form(deskItem(0), N2)</var> cost <code>x</code>,
we have the following proportion:
</p>
<p><code>\qquad \dfrac{<var>N2</var>}{x}</code></p>
<p>
We can write the fact that <code><var>N1</var></code> <var>plural_form(deskItem(0), N1)</var>
cost <code>\$<var>C</var></code> as a proportion:
</p>
<p><code>\qquad \dfrac{<var>N1</var>}{\$<var>C</var>}</code></p>
<p>
The cost changes along with the number of <var>plural_form(deskItem(0))</var> purchased,
and so the two proportions are equivalent.
</p>
<p><code>\qquad <var>SOLUTION</var></code></p>
</div>
</div>
<div data-type="original" data-weight="3">
<div class="vars">
<var id="SOLUTION">"\\dfrac{" + N1 + "}{" + N2 + "} = \\dfrac{\\$" + C + "}{x}"</var>
</div>
<div class="hints">
<p>
We know the cost of <code><var>N1</var></code> <var>plural_form(deskItem(0), N1)</var>.
We want to know the cost of <code><var>N2</var></code> <var>plural_form(deskItem(0), N2)</var>.
We can write the numbers of <var>plural_form(deskItem(0))</var> as a proportion:
</p>
<p><code>\qquad \dfrac{<var>N1</var>}{<var>N2</var>}</code></p>
<p>
We know <code><var>N1</var></code> <var>plural_form(deskItem(0), N1)</var> costs <code>\$<var>C</var></code>.
We can let <code>x</code> represent the unknown cost of <code><var>N2</var></code> <var>plural_form(deskItem(0), N2)</var>.
The proportion of these costs can be expressed as:
</p>
<p><code>\qquad \dfrac{\$<var>C</var>}{x}</code></p>
<p>
The cost changes along with the number of <var>plural_form(deskItem(0))</var> purchased,
and so the two proportions are equivalent.
</p>
<p><code>\qquad <var>SOLUTION</var></code></p>
</div>
</div>
<div data-type="original" data-weight="1">
<div class="vars">
<var id="SOLUTION">"\\dfrac{x}{" + N2 + "} = \\dfrac{\\$" + C + "}{" + N1 + "}"</var>
</div>
<div class="hints">
<p>
If we let <code>x</code> represent the cost of <code><var>N2</var></code> <var>plural_form(deskItem(0), N2)</var>,
we have the following proportion:
</p>
<p><code>\qquad \dfrac{x}{<var>N2</var>}</code></p>
<p>
We have to pay <code>\$<var>C</var></code> for <code><var>N1</var></code> <var>plural_form(deskItem(0), N1)</var>,
and that can be written as a proportion:
</p>
<p><code>\qquad \dfrac{\$<var>C</var>}{<var>N1</var>}</code></p>
<p>Since the price per <var>deskItem(0)</var> stays the same, these two proportions are equivalent.</p>
<p><code>\qquad <var>SOLUTION</var></code></p>
</div>
</div>
</div>
</div>
</body>
</html>