Question 1170790
Anne's present age = a
Mia's present age = a - 4
<pr>
(a - 4 - 1)(a + 1) = 315
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(a - 5)(a + 1) = 315
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a² - 4a - 5 = 315
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a² - 4a - 320 = 0
<pr>
(a - 20)(a + 16) = 0
<pr>
a = 20, -16
<pr>
Since it is impossible that Anne's current age is -16, we can eliminate that result.  Therefore, we are left with a = 20
<pr>
Anne's present age = a = <b>20</b>
Mia's present age = a - 4 = 20 - 4 = <b>16</b>
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Check it:
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<i>Mia is four years younger than Anne.</i>
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Mia is 16 and Anne is 20.  So, that checks.
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<i>The product of her (Mia's) age last year and Anne's age next year will be 315.</i>
<pr>
Mia's age last year was 15.  Anne's age next year will be 21.
<pr>
15 * 21 = 315.  So, that checks.