Question

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?​

Answer 1

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

Emily's age = 15 years

Tuli's age = 15 - 10 = 5 years

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.