SOLUTION: 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.

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.
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
Anne's present age = a
Mia's present age = a - 4

(a - 4 - 1)(a + 1) = 315

(a - 5)(a + 1) = 315

a² - 4a - 5 = 315

a² - 4a - 320 = 0

(a - 20)(a + 16) = 0

a = 20, -16

Since it is impossible that Anne's current age is -16, we can eliminate that result. Therefore, we are left with a = 20

Anne's present age = a = 20
Mia's present age = a - 4 = 20 - 4 = 16

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Check it:

Mia is four years younger than Anne.

Mia is 16 and Anne is 20. So, that checks.

The product of her (Mia's) age last year and Anne's age next year will be 315.

Mia's age last year was 15. Anne's age next year will be 21.

15 * 21 = 315. So, that checks.
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