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:
[tex]\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=\frac{-20}{-2} \\ y=10 \end{gathered}[/tex]So, the daughters' ages are 10 and 14 years old.
Answer: Letter C
