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4 September, 00:02

Tuli is 10 years younger than Emily. The product of their

ages 2 years ago was 39. Let the present age of Emily

be A. Which of the following quadratic equations does A

satisfy?

+1
Answers (1)
  1. 4 September, 02:50
    0
    a² - 14a - 15 = 0 (quadratic equation)

    Emily's age = 15 years

    Tuli's age = 15 - 10 = 5 years

    Step-by-step explanation:

    let

    Emily age = a

    Tuli age = a - 10

    Two years ago their ages will be as follows.

    Emily's age = a - 2

    Tuli's age = a - 10 - 2 = a - 12

    The product of their ages 2 years ago is 39.

    (a - 2) (a - 12) = 39

    a² - 12a - 2a + 24 - 39 = 0

    a² - 14a - 15 = 0 (quadratic equation)

    To get a

    a² + a - 15a - 15 = 0

    a (a + 1) - 15 (a + 1)

    (a + 1) (a - 15)

    a = - 1 or 15

    we can only use 15 as it is positive.
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