Math CentralQuandaries & Queries


Question from Sam, a student:

Kate is 16 yrs. younger then Tess. Nina is 8 yrs. older then Kate. The sum of their ages is 189. How old is each?

HI Sam,

This is an algebra problem so I need a variable to stand for the age of one of these women. I want the variable to stand for the age of the youngest woman so that the ages of the other two will be the age of the youngest plus something. If I let the variable stand for the age of one of the other two then the age of the youngest will be that age minus something, and I would rather not have to deal with subtraction.

Read the question. Kate is younger than Tess and Nina is older than Kate so Kate is the youngest. Thus I would start this way.

Let $K$ be Kate's age. Since Kate is 16 years younger than Tess, Tess' age is $K + 16.$ How old is Nina? The sum of the three ages is $189.$ Solve for $K.$


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