Question

Mr. Thaxton has two daughters. The sum of their ages is twenty-one. The product of their ages is one hundred ten. How old is Mr. Thaxton's youngest daughter?

A.
9


B.
10


C.
11


D.
12

Answer 1

B. 10

Explanation:

x + y = 21

xy = 110

Rewrite first equation. x + y = 21 becomes y = -x + 21

Now substitute this new equation in the second equation.

x(-x+21) = 110

-x^2 + 21x - 110

Divide by -1

x^2 - 21x + 110

(x - 10)(x - 11)

x = 10, 11

10 is less, so the youngest daughter is 10