Question

Ms. Jenkins Has two daughters. The sum of their ages is twenty-four. The product of their ages is one hundred forty. How old is Ms. Jenkins’ oldest daughter?A) 10B) 12 C) 14 D) 16

Answer 1

Ms. Jenkins Has two daughters. The sum of their ages is twenty-four. The product of their ages is one hundred forty. How old is Ms. Jenkins’ oldest daughter?

Let the youngest daughter's age be y and the oldest be x.

x + y = 24

x*y = 140

Let's solve the system of equations using the substitution method:

x + y = 24

x*y = 140

x = 24-y

(24-y)*y = 140

24y-y²-140 = 0

-y²+24y -140 = 0

Now we're going to use the quadratic formula to solve the equation:

`\begin{gathered} y=\frac{-b\pm\sqrt[]{b^(2)-4ac}_{}}{2a} \\ y=\frac{-24\pm\sqrt[]{576-4\cdot-1\cdot-140}}{-2} \\ y=\frac{-24\pm\sqrt[]{16}}{-2} \\ y=(-20)/(-2) \\ y=10 \end{gathered}`

So, the daughters' ages are 10 and 14 years old.

Answer: Letter C