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<!DOCTYPE html>
<html data-require="math math-format word-problems khanscript">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Linear equation and inequality word problems</title>
<script data-main="../local-only/main.js" src="../local-only/require.js"></script>
</head>
<body>
<div class="exercise">
<script type="text/khanscript">
Khan.scratchpad.disable();
</script>
<div class="problems">
<div id="magazine_subscription_selling">
<div class="vars" data-ensure="Q &lt; R">
<var id="Q">randRange(20, 40)</var>
<var id="P">randRange(2, 10)</var>
<var id="R">randRange(30, 100)</var>
<var id="X">ceil((R - Q) / P)</var>
</div>
<p class="problem" data-if="isMale(1)">
<var>person(1)</var> sells magazine subscriptions and earns
<code>$<var>P</var></code> for every new subscriber
he signs up. <var>person(1)</var> also earns a
<code>$<var>Q</var></code> weekly bonus regardless of how many
magazine subscriptions he sells.
</p><p class="problem" data-else="">
<var>person(1)</var> sells magazine subscriptions and earns
<code>$<var>P</var></code> for every new subscriber
she signs up. <var>person(1)</var> also earns a
<code>$<var>Q</var></code> weekly bonus regardless of how many
magazine subscriptions she sells.
</p>
<p class="question" data-if="isMale(1)">
If <var>person(1)</var> wants to earn at least
<code>$<var>R</var></code> this week, what is the minimum
number of subscriptions he needs to sell?
</p><p class="question" data-else="">
If <var>person(1)</var> wants to earn at least
<code>$<var>R</var></code> this week, what is the minimum
number of subscriptions she needs to sell?
</p>
<div class="solution" data-type="custom">
<div class="instruction">
<input type="text" id="guessans"> subscriptions
</div>
<div class="guess">[
$("#guessans").val(),
$("#firsttext").val(),
$("#secondtext").val()
]</div>
<div class="validator-function">
var correct = X;
var solutionDiv = $("&lt;div&gt;").text(correct);
var validator = Khan.answerTypes.number.createValidator(solutionDiv);
return validator(guess[0]);
</div>
<div class="show-guess-solutionarea">
if (guess != null) {
$("#guessans").val(guess[0]);
}
else {
$("#guessans").val("");
if ($("#firsttext").length &gt; 0) {
$("#firsttext").text("");
$("#secondtext").text("");
}
}
</div>
<div class="show-guess">
if (guess != null &amp;&amp; $("#firsttext").length &gt; 0) {
guess[1] === null ? $("#firsttext").text("") : $("#firsttext").text(guess[1]);
guess[2] === null ? $("#secondtext").text("") : $("#secondtext").text(guess[2]);
}
</div>
</div>
<div class="hints">
<p>To solve this, let's set up an expression to show how much
money <var>person(1)</var> will make.</p>
<p>
<span>Amount earned this week <code>=</code></span><br>
<span><code>\qquad</code>Subscriptions sold
<code>\times</code> Price per subscription
<code>+</code> Weekly bonus</span>
</p>
<p>Since <var>person(1)</var> wants to make
<strong>at least</strong> <code>$<var>R</var></code> this
week, we can turn this into an inequality.</p>
<div>
<p>Amount earned this week
<code>\geq $<var>R</var></code></p>
<p>Subscriptions sold <code>\times</code> Price per
subscription <code>+</code> Weekly bonus
<code>\geq $<var>R</var></code></p>
</div>
<p>We are solving for the number of subscriptions sold, so let
subscriptions sold be represented by the variable
<code>x</code>.</p>
<div>
<p>We can now plug in:</p>
<p><code>x \cdot $<var>P</var> + $<var>Q</var> \geq
$<var>R</var></code></p>
</div>
<div>
<p><code>
x \cdot $<var>P</var> \geq
$<var>R</var> - $<var>Q</var>
</code></p>
<p><code>
x \cdot $<var>P</var> \geq $<var>R - Q</var>
</code></p>
</div>
<div data-if="(R - Q) % P !== 0" data-unwrap="">
<p><code>x \geq \dfrac{<var>R - Q</var>}{<var>P</var>}
\approx <var>localeToFixed((R - Q) / P, 2)</var></code></p>
<p data-if="(R - Q) % P !== 0">
Since <var>person(1)</var> cannot sell parts of
subscriptions, we round
<code><var>localeToFixed((R - Q) / P, 2)</var></code> up to
<code><var>X</var></code>.
</p>
</div>
<div data-else="">
<p><code>x \geq \dfrac{<var>R - Q</var>}{<var>P</var>} =
<var>(R - Q) / P</var></code></p>
</div>
<p><var>person(1)</var> must sell at least <var>X</var>
subscriptions this week.</p>
</div>
</div>
<div id="video_game_levels">
<div class="vars" data-ensure="Q &lt; R">
<var id="Q">10 * randRange(100 / 10, 500 / 10)</var>
<var id="P">10 * randRange(300 / 10, 1000 / 10)</var>
<var id="R">10 * randRange(2000 / 10, 4000 / 10)</var>
<var id="X">ceil((R - Q) / P)</var>
</div>
<p class="problem" data-if="isMale(1)">
For every level <var>person(1)</var> completes in
his favorite game, he earns
<code><var>P</var></code> points. <var>person(1)</var> already
has <code><var>Q</var></code> points in the game and wants to
end up with at least <code><var>R</var></code> points before
he goes to bed.
</p><p class="problem" data-else="">
For every level <var>person(1)</var> completes in
her favorite game, she earns
<code><var>P</var></code> points. <var>person(1)</var> already
has <code><var>Q</var></code> points in the game and wants to
end up with at least <code><var>R</var></code> points before
she goes to bed.
</p>
<p class="question" data-if="isMale(1)">
Assuming <var>person(1)</var> can only get points by completing levels,
what is the minimum number of levels that he needs to complete
to reach his goal?
</p><p class="question" data-else="">
Assuming <var>person(1)</var> can only get points by completing levels,
what is the minimum number of levels that she needs to complete
to reach her goal?
</p>
<div class="solution" data-type="custom">
<div class="instruction">
<input type="text" id="guessans"> levels
</div>
<div class="guess">[
$("#guessans").val(),
$("#firsttext").val(),
$("#secondtext").val()
]</div>
<div class="validator-function">
var correct = X;
var solutionDiv = $("&lt;div&gt;").text(correct);
var validator = Khan.answerTypes.number.createValidator(solutionDiv);
return validator(guess[0]);
</div>
<div class="show-guess-solutionarea">
if (guess != null) {
$("#guessans").val(guess[0]);
}
else {
$("#guessans").val("");
if ($("#firsttext").length &gt; 0) {
$("#firsttext").text("");
$("#secondtext").text("");
}
}
</div>
<div class="show-guess">
if (guess != null &amp;&amp; $("#firsttext").length &gt; 0) {
guess[1] === null ? $("#firsttext").text("") : $("#firsttext").text(guess[1]);
guess[2] === null ? $("#secondtext").text("") : $("#secondtext").text(guess[2]);
}
</div>
</div>
<div class="hints">
<p>To solve this, let's set up an expression to show how many
points <var>person(1)</var> will have after each level.</p>
<p>
<span>Number of points <code>=</code></span><br>
<span><code>\qquad</code>Levels completed
<code>\times</code> Points per level <code>+</code>
Starting points</span>
</p>
<p>
Since <var>person(1)</var> wants to have
<strong>at least</strong> <code><var>R</var></code> points
before going to bed, we can set up an inequality.
</p>
<div>
<p>Number of points <code>\geq <var>R</var></code></p>
<p>Levels completed <code>\times</code> Points per level
<code>+</code> Starting points <code>\geq
<var>R</var></code></p>
</div>
<p>We are solving for the number of levels to be completed, so
let the number of levels be represented by the variable
<code>x</code>.</p>
<div>
<p>We can now plug in:</p>
<p><code>x \cdot <var>P</var> + <var>Q</var> \geq
<var>R</var></code></p>
</div>
<div>
<p><code>
x \cdot <var>P</var> \geq <var>R</var> - <var>Q</var>
</code></p>
<p><code>
x \cdot <var>P</var> \geq <var>R - Q</var>
</code></p>
</div>
<div data-if="(R - Q) % P !== 0" data-unwrap="">
<p><code>x \geq \dfrac{<var>R - Q</var>}{<var>P</var>}
\approx <var>localeToFixed((R - Q) / P, 2)</var></code></p>
<p data-if="(R - Q) % P !== 0"><span data-if="isMale(1)" data-unwrap="">
Since <var>person(1)</var> won't get points unless
he completes the entire level, we round
<code><var>localeToFixed((R - Q) / P, 2)</var></code> up to
<code><var>X</var></code>.
</span><span data-else="" data-unwrap="">
Since <var>person(1)</var> won't get points unless
she completes the entire level, we round
<code><var>localeToFixed((R - Q) / P, 2)</var></code> up to
<code><var>X</var></code>.
</span></p>
</div>
<div data-else="">
<p><code>x \geq \dfrac{<var>R - Q</var>}{<var>P</var>} =
<var>(R - Q) / P</var></code></p>
</div>
<p><var>person(1)</var> must complete at least <var>X</var>
levels.</p>
</div>
</div>
<div id="piano_months">
<div class="vars" data-ensure="Q &lt; R">
<var id="Q">randRange(5, 50)</var>
<var id="R">randRange(50, 200)</var>
<var id="P">randRange(1, 10)</var>
<var id="X">ceil(( R - Q ) / P)</var>
</div>
<p class="problem" data-if="isMale(1)">
To move up to the maestro level in his piano
school, <var>person(1)</var> needs to master at least
<code><var>R</var></code> songs. <var>person(1)</var> has
already mastered <code><var>Q</var></code> songs.
</p><p class="problem" data-else="">
To move up to the maestro level in her piano
school, <var>person(1)</var> needs to master at least
<code><var>R</var></code> songs. <var>person(1)</var> has
already mastered <code><var>Q</var></code> songs.
</p>
<p class="question">
If <var>person(1)</var> can master
<code><var>P</var></code> songs per month, what is the minimum
number of months it will take <var>him(1)</var> to move to the
maestro level?
</p>
<div class="solution" data-type="custom">
<div class="instruction">
<input type="text" id="guessans"> months
</div>
<div class="guess">[
$("#guessans").val(),
$("#firsttext").val(),
$("#secondtext").val()
]</div>
<div class="validator-function">
var correct = X;
var solutionDiv = $("&lt;div&gt;").text(correct);
var validator = Khan.answerTypes.number.createValidator(solutionDiv);
return validator(guess[0]);
</div>
<div class="show-guess-solutionarea">
if (guess != null) {
$("#guessans").val(guess[0]);
}
else {
$("#guessans").val("");
if ($("#firsttext").length &gt; 0) {
$("#firsttext").text("");
$("#secondtext").text("");
}
}
</div>
<div class="show-guess">
if (guess != null &amp;&amp; $("#firsttext").length &gt; 0) {
guess[1] === null ? $("#firsttext").text("") : $("#firsttext").text(guess[1]);
guess[2] === null ? $("#secondtext").text("") : $("#secondtext").text(guess[2]);
}
</div>
</div>
<div class="hints">
<p>To solve this, let's set up an expression to show how many
songs <var>person(1)</var> will have mastered after each
month.</p>
<p>
<span>Number of songs mastered <code>=</code></span><br>
<span><code>\quad</code>Months at school
<code>\times</code> Songs mastered per month
<code>+</code> Songs already mastered</span>
</p>
<p>
Since <var>person(1)</var> Needs to have
<strong>at least</strong> <code><var>R</var></code> songs
mastered to move to maestro level, we can set up an
inequality to find the number of months needed.
</p>
<div>
<p>Number of songs mastered <code>\geq
<var>R</var></code><br>
</p><p>
<span>Months at school <code>\times</code> Songs mastered
per month</span><br>
<span><code>\qquad+</code> Songs already mastered
<code>\geq <var>R</var></code></span>
</p>
</div>
<p>We are solving for the months spent at school, so let the
number of months be represented by the variable
<code>x</code>.</p>
<div>
<p>We can now plug in:</p>
<p><code>x \cdot <var>P</var> + <var>Q</var> \geq
<var>R</var></code></p>
</div>
<div>
<p><code>
x \cdot <var>P</var> \geq <var>R</var> - <var>Q</var>
</code></p>
<p><code>
x \cdot <var>P</var> \geq <var>R - Q</var>
</code></p>
</div>
<div data-if="(R - Q) % P !== 0" data-unwrap="">
<p><code>x \geq \dfrac{<var>R - Q</var>}{<var>P</var>}
\approx <var>localeToFixed((R - Q) / P, 2)</var></code></p>
<p data-if="(R - Q) % P !== 0">
Since we only care about whole months that
<var>person(1)</var> has spent working, we round
<code><var>localeToFixed((R - Q) / P, 2)</var></code> up to
<code><var>X</var></code>.
</p>
</div>
<div data-else="">
<p><code>x \geq \dfrac{<var>R - Q</var>}{<var>P</var>} =
<var>(R - Q) / P</var></code></p>
</div>
<p><var>person(1)</var> must work for at least <var>X</var>
months.</p>
</div>
</div>
</div>
</div>
</body>
</html>
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