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129 lines
5.9 KiB
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129 lines
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<h1 class="puzTitle">Kate and her Son's Age Puzzle - Solution</h1>
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<div class="puzPuzzle"><h2>The Puzzle:</h2>
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<div class="puzText">
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<div class="puzThumb"><img src="images/algebra.gif" width="120" height="61" alt="Kate and her Son's Age" style="border-style: none" /></div>
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5 years ago Kate was 5 times as old as her Son. <br />
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<br />
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In 5 years her age will be 8 less than three times her Son's age at that time. <br />
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<br />
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Find their ages.<br />
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<br />
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<br />
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(Puzzle contributed by "Pratibha")</div>
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<div class="puzSep"></div>
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<div class="puzSoln"><h2>Our Solution:</h3>
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<div class="puzSolnText">First draw a table like this one below:<br />
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<table border="0" cellpadding="5"><br />
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<tr><th> </th><th>5 YRS AGO</th><th>PRESENT</th><th>5 YRS LATER</th></tr><br />
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<tr><td>KATE</td><td>5x</td><td>5x + 5</td><td>5x + 10</td></tr><br />
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<tr><td>SON</td><td>x</td><td>x + 5</td><td>x + 10</td></tr><br />
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</table><br />
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<br />
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Now we know that in 5 years her age will be 8 less than three times her Son's age at that time. <br />
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<br />
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So, if we add 8 to (Kate's age 5 years from now), it will be equal to 3 times (her Son's age 5 years from now) and then we can use algebra to solve it! <br />
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<br />
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So:<br />
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<br />
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(5x + 10) + 8 = 3(x + 10)<br />
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5x + 18 = 3x + 30<br />
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5x - 3x = 30 - 18<br />
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2x = 12<br />
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x = 12 / 2<br />
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x = 6<br />
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<br />
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Now Kate's Present age is 5x + 5<br />
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=> 5(6) + 5<br />
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= 30 + 5<br />
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= 35 YEARS!!<br />
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<br />
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Now her Son's Present age is x + 5<br />
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=> 6 + 5<br />
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= 11 YEARS!!<br />
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<br />
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SOLVED!<br />
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<br />
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<br />
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<br />
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(Solution contributed by "Pratibha")</div></div>
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<div class="puzSolnFtr">Try more <a href="algebra-puzzles-index.html">Algebra Puzzles</a><br>See this puzzle <a href="kate-and-her-son-s-age.html">without solution</a><br></div>
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