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

The age of Ms. Jenkins oldest daughter is 14.

Step-by-step 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].

0 + 24 = 24 1 + 23 = 24 2 + 22 = 24 3 + 21 = 24 4 + 20 = 24 5 + 19 = 24 6 + 18 = 24 7 + 17 = 24 8 + 16 = 24 9 + 15 = 24 10 + 14 = 24 11 + 13 = 24 12 + 12 = 24

If we continued listing numbers, we would repeat numbers that are already listed, so we can stop there.

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

0 x 24 = 0 1 x 23 = 23 2 x 22 = 44 3 x 21 = 63 4 x 20 = 80 5 x 19 = 95 6 x 18 = 108 7 x 17 = 119 8 x 16 = 128 9 x 15 = 135 10 x 14 = 140 11 x 13 = 143 12 x 12 = 144

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.