Math CentralQuandaries & Queries


Question from Nakyi:

The sum of Sabrina’s age and twice her sister’s age is equal to their mom’s
Age. If Sabrina’s sister is two years older than her and their mom is 37, how old is Sabrina?


I would start with a guess. Suppose Sabrina is $15$ years old. In that case her sister is $15 + 2$ years old. The sum of Sabrina's age and twice her sisters age is

\[15 + 2 \times (15 + 2) = 15 + 30 + 4 = 49.\]

I was hoping this would be 37, her mother's age so my guess didn't work.

Now let's try the same procedure using some algebra.

Suppose Sabrina is $x$ years old. How old is he sister? Write the algebraic expression for the sum of Sabrina's age and twice her sister's age. This sum needs to be 37 and hence you have an equation. Solve for $x.$

Make sure you verify your answer,

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