document.write( "Question 1170790: Mia is four years younger than Anne. The product of her age last year and Anne's age next year will be 315. Find their present ages. \n" ); document.write( "

Algebra.Com's Answer #795677 by VFBundy(438) $\"\"$ $\"About$

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Anne's present age = a
\n" ); document.write( "Mia's present age = a - 4
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\n" ); document.write( "(a - 4 - 1)(a + 1) = 315
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\n" ); document.write( "(a - 5)(a + 1) = 315
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\n" ); document.write( "a² - 4a - 5 = 315
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\n" ); document.write( "a² - 4a - 320 = 0
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\n" ); document.write( "(a - 20)(a + 16) = 0
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\n" ); document.write( "a = 20, -16
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\n" ); document.write( "Since it is impossible that Anne's current age is -16, we can eliminate that result. Therefore, we are left with a = 20
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\n" ); document.write( "Anne's present age = a = 20
\n" ); document.write( "Mia's present age = a - 4 = 20 - 4 = 16
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\n" ); document.write( "Check it:
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\n" ); document.write( "Mia is four years younger than Anne.
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\n" ); document.write( "Mia is 16 and Anne is 20. So, that checks.
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\n" ); document.write( "The product of her (Mia's) age last year and Anne's age next year will be 315.
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\n" ); document.write( "Mia's age last year was 15. Anne's age next year will be 21.
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\n" ); document.write( "15 * 21 = 315. So, that checks. \n" ); document.write( "

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