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. Jenkie‘s oldest daughter?A) 10B) 12 C) 14D) 16

Answer 1

Explanation:

First: List addition sentences that include all of the whole numbers that could equal 24:

Why should we do that? To find out what numbers have a sum of 24. Any of the two numbers that make up the addition equation could be the ages of Ms. Jenkins' daughters [and the bigger number; our answer].

Second: Find out which of the two numbers that make up the addition equation have a product (multiplication answer) of 140:

Let the first daughter age = x and the second daughter age = y

Sum of their age = x+y = 24

product of their age =xy = 140

`\begin{gathered} x+y=24\ldots\ldots(1) \\ xy=140\ldots\ldots\text{.(2)} \\ from\text{ equat(1) } \\ x=24-y \end{gathered}`

Sub the value of x in equation 2

`\begin{gathered} (24-y)y=140 \\ 24y-y^2=140 \\ y^2-24y+140=0 \\ y^2-10y-14y+140=0 \\ y(y-10)-14(y-10)=0 \\ (y-10)(y-14)=0 \\ y-10=0,y-14=0 \\ y=10,y=14 \end{gathered}`

10 x 14 equals 140, and 10 + 14 = 140. These two numbers meet all of the conditions of the question. Now, which one is bigger [or which sister's age is older] 10 or 14. 14 is obviously bigger so 14 is the age of Ms. Jenkins' oldest daughter.

Hence the age of Ms. Jenkins oldest daughter is 14