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<!DOCTYPE html>
<html data-require="math math-format graphie graphie-helpers word-problems spin">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Negative number word problems</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="problems">
<div id="february_afternoon_result">
<div class="vars">
<var id="X">randRange( -20, -1 )</var><!-- Afternoon temperature -->
<var id="Y">randRange( 5, 30 )</var><!-- Temperature change -->
<var id="Z">X - Y</var><!-- Final temperature -->
</div>
<p class="problem spin">{This afternoon, an outdoor temperature had a reading of|On a cold February afternoon, the temperature outside was} <var>abs( X )</var> degrees below zero. {By evening, the temperature had dropped by|In the evening, you take a quick look at the thermometer, and see that the temperature had dropped by} <var>Y</var> degrees.</p>
<p class="question">What was the temperature in the evening?</p>
<div class="solution" data-type="multiple">
<p><span class="sol" data-forms="integer"><var>Z</var></span> degrees</p>
</div>
<div class="hints">
<p><code><var>abs( X )</var></code> degrees below zero is the same as <code><var>X</var>^{\circ}</code>.</p>
<div>
<p>Since the temperature dropped by <code><var>Y</var>^{\circ}</code>, subtract this amount from the afternoon temperature.</p>
<p><code><var>X</var>^{\circ} - <var>Y</var>^{\circ} = <var>Z</var>^{\circ}</code></p>
</div>
<p>The temperature in the evening was <code><var>Z</var>^{\circ}</code>.</p>
</div>
</div>
<div id="sledding_delta">
<div class="vars">
<var id="X">randRange( -30, -15 )</var><!-- Initial temperature -->
<var id="Z">randRange( -10, 20 )</var><!-- Final temperature -->
<var id="Y">Z - X</var><!-- Temperature change -->
</div>
<p class="problem spin">{When <var>person( 1 )</var> went outside to go sledding in the morning|As <var>person( 1 )</var> prepared for <var>his( 1 )</var> daily sledding practice}, <var>he( 1 )</var> {looked at the thermometer and saw|heard on the radio} that the temperature was <var>abs( X )</var> degrees below zero. {After sledding for <var>plural( randRange( 1, 8 ), "hour" )</var>,|After a long day of sledding <var>he( 1 )</var> saw that} the temperature was now <var>Z</var> degrees.</p>
<p class="question">By how many degrees had the temperature increased?</p>
<div class="solution" data-type="multiple">
<p><span class="sol" data-forms="integer"><var>Y</var></span> degrees</p>
</div>
<div class="hints">
<p><code><var>abs( X )</var></code> degrees below zero is the same as <code><var>X</var>^{\circ}</code>.</p>
<p>Change in temperature = final temperature - initial temperature</p>
<p>Change in temperature = <code><var>Z</var>^{\circ} - (<var>X</var>^{\circ}) = <var>Z</var>^{\circ} - <var>X</var>^{\circ} = <var>Y</var>^{\circ}</code></p>
<p>The temperature had increased by <code><var>Y</var>^{\circ}</code>.</p>
</div>
</div>
<div id="scuba_result">
<div class="vars">
<var id="X">randRange( 25, 40 )</var><!-- Initial level -->
<var id="Y">randRange( 20, 35 )</var><!-- Diving distance -->
<var id="Z">-X - Y</var><!-- Final position -->
</div>
<p class="problem spin"><var>person( 1 )</var> was scuba diving <var>X</var> meters below sea level when <var>he( 1 )</var> spotted a beautiful fish below. {From a distance, the fish looked to be about <var>randRange( 25, 35 )</var> cm wide. |}{To take a proper photograph|To see the fish up close}, <var>person( 1 )</var> dove <var>Y</var> meters until <var>he( 1 )</var> was level with the fish, staring into its eyes.</p>
<p class="question">Where was the fish relative to sea level?</p>
<div class="solution" data-type="multiple">
<p><span class="sol" data-forms="integer"><var>Z</var></span> meters</p>
</div>
<div class="hints">
<p><var>person( 1 )</var> was initially <code><var>X</var></code> meters below sea level, which can be written as a negative number, <code>-<var>X</var></code> meters.</p>
<p><var>person( 1 )</var> dove down <code><var>Y</var></code> meters, so we can subtract that distance from <var>person( 1 )</var>’s initial level to find out where the fish is.</p>
<p>Fish’s position relative to sea level <code>=-<var>X</var>\text{ meters} - <var>Y</var>\text{ meters} = <var>Z</var>\text{ meters}</code></p>
</div>
</div>
<div id="dolphin_delta">
<div class="vars">
<var id="X">randRange( 5, 20 )</var><!-- Below sea level -->
<var id="Y">randRange( 5, 10 )</var><!-- Above sea level -->
<var id="Z">Y + X</var><!-- Distance travelled -->
</div>
<p class="problem spin">A spinner dolphin jumped from <var>X</var> meters below sea level and flipped through the air at <var>Y</var> meters above sea level. {The jump itself took about 1.<var>randRange( 1, 9 )</var> seconds.|}</p>
<p class="question">How many meters did the dolphin travel to reach the highest point of the jump?</p>
<div class="solution" data-type="multiple">
<p><span class="sol" data-forms="integer"><var>Z</var></span> meters</p>
</div>
<div class="hints">
<p>The dolphin was initially <var>X</var> meters below sea level, which can be written as a negative number, -<var>X</var> meters.</p>
<p>Distance the dolphin jumped = final position - initial position</p>
<p><code><var>Y</var>\text{ meters} - (-<var>X</var>\text{ meters}) = <var>Y</var>\text{ meters} + <var>X</var>\text{ meters} = <var>Z</var>\text{ meters}</code></p>
</div>
</div>
<div id="baseball_camp_result">
<div class="vars" data-ensure="N * COST < X">
<var id="X">randRange( 10000, 50000 )</var><!-- Loan amount -->
<var id="N">randRange( 10, 50 )</var><!-- # of campers -->
<var id="COST">randRange( 100, 500 )</var><!-- Cost per camper -->
<var id="Y">N * COST</var><!-- Amount earned from campers -->
<var id="Z">X - Y</var><!-- Money owed -->
</div>
<p class="problem spin"><var>person( 1 )</var> received a loan of $<var>commafy( X )</var> from the bank to start a baseball camp. <var>person( 1 )</var> used the loan to rent baseball bats, mitts, and baseballs for the summer, and to pay the coaches’ salaries. Over the course of the summer, <var>N</var> campers attended <var>person( 1 )</var>’s baseball camp, and each camper paid a fee of $<var>COST</var> to attend. <var>person( 1 )</var> used all of the money from the campers’ fees to start paying back the loan.</p>
<p class="question">At the end of the summer what was <var>person( 1 )</var>'s net worth, assuming <var>he( 1 )</var> had no other assets or liabilities?</p>
<div class="solution" data-forms="dollar"><var>-1 * Z</var></div>
<div class="hints">
<p><var>person( 1 )</var> started out the summer with <code>$<var>commafy( X )</var></code> of debt, which can be represented as a negative number, <code>-$<var>commafy( X )</var></code>.</p>
<p>Amount of money <var>person( 1 )</var> earned from campers = <code><var>N</var> \times $<var>COST</var>=$<var>commafy( Y )</var></code></p>
<p>debt + earnings = <var>person( 1 )</var>'s account balance</p>
<p><code>-$<var>commafy( X )</var> + $<var>commafy( Y )</var> = -$<var>commafy( Z )</var></code></p>
</div>
</div>
</div>
</div>
</body>
</html>
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