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<title>A.I.14.8</title>
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<b>Feladat: 14.8.</b><br /> <a name="algI_GHP_237" />[<a href="bib_box.php?mode=sne-s-j-&amp;citation_num=65" target="bib_box" onclick="mutat('bib_box.php?mode=sne-s-j-&amp;citation_num=65'); return false;">65</a>] Hány éves az, aki ezt mondja: ,,3 év múlva feleannyi idős leszek,

hat éve pedig harmadannyi idős voltam, mint amennyi Péter most"?

Válasszuk ki, hogy a kérdezett <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>k</m:mi></m:mrow></m:math> kor (évben) melyik halmazba esik!

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<br /><b>A)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>0</m:mn><m:mo>&le;</m:mo><m:mi>k</m:mi><m:mo>&lt;</m:mo><m:mn>14</m:mn></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>B)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>14</m:mn><m:mo>&le;</m:mo><m:mi>k</m:mi><m:mo>&lt;</m:mo><m:mn>21</m:mn></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>C)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>21</m:mn><m:mo>&le;</m:mo><m:mi>x</m:mi><m:mo>&lt;</m:mo><m:mn>28</m:mn></m:mrow></m:math>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>D)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>28</m:mn><m:mo>&le;</m:mo><m:mi>k</m:mi><m:mo>&lt;</m:mo><m:mn>35</m:mn></m:mrow></m:math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<b>E)</b>&nbsp;&nbsp;&nbsp; <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>35</m:mn><m:mo>&le;</m:mo><m:mi>k</m:mi></m:mrow></m:math><br />

y default: it reads from stdin and writes to stdout.

But a non-switch argument specifies the file[.tex] to translate to file.xml.

Diagnostics concerning unknown or untranslated constructs are sent to stderr.

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<a name="_solution_algI_GHP_237" /><b>Megoldás: 14.8</b><br />
<b>C</b>

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Legyen jelenlegi korom <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>k</m:mi></m:mrow></m:math>. Három év múlva <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>k</m:mi><m:mo>+</m:mo><m:mn>3</m:mn></m:mrow></m:math> éves leszek, tehát Péter mostani kora <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>2</m:mn><m:mo stretchy="false">(</m:mo><m:mi>k</m:mi><m:mo>+</m:mo><m:mn>3</m:mn><m:mo stretchy="false">)</m:mo></m:mrow></m:math>. Hat évvel ezelőtt <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>k</m:mi><m:mo>-</m:mo><m:mn>6</m:mn></m:mrow></m:math> éves voltam, amiből Péter jelenlegi kora 

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>3</m:mn><m:mo stretchy="false">(</m:mo><m:mi>k</m:mi><m:mo>-</m:mo><m:mn>6</m:mn><m:mo stretchy="false">)</m:mo></m:mrow></m:math>. Péter korát kétféleképpen is felírtuk: 

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    <m:math xmlns="http://www.w3.org/1998/Math/MathML">

    <m:mstyle displaystyle="true"><m:mrow><m:mn>2</m:mn><m:mo stretchy="false">(</m:mo><m:mi>k</m:mi><m:mo>+</m:mo><m:mn>3</m:mn><m:mo stretchy="false">)</m:mo><m:mo>=</m:mo><m:mn>3</m:mn><m:mo stretchy="false">(</m:mo><m:mi>k</m:mi><m:mo>-</m:mo><m:mn>6</m:mn><m:mo stretchy="false">)</m:mo><m:mo>&rArr;</m:mo><m:mn>2</m:mn><m:mi>k</m:mi><m:mo>+</m:mo><m:mn>6</m:mn><m:mo>=</m:mo><m:mn>3</m:mn><m:mi>k</m:mi><m:mo>-</m:mo><m:mn>18</m:mn><m:mo>&rArr;</m:mo><m:mn>24</m:mn><m:mo>=</m:mo><m:mi>k</m:mi><m:mo>.</m:mo></m:mrow>

    </m:mstyle></m:math>

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Tehát 24 éves az, akitől idézett a feladat. Péter 54 éves, három év múlva valóban feleannyi idős lesz (27), hat éve pedig harmadannyi (18) volt a szóbanforgó személy.
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