Question

Sam is 10 years younger than one-half the age of his aunt. Let a represent his aunt’s age. Which algebraic expression can be used to determine Sam’s age if his aunt is 40?
StartFraction a Over 10 EndFraction minus 2; when a = 40 Sam is 2 years old
StartFraction a Over 10 EndFraction + 2; when a = 40 Sam is 6 years old
StartFraction a Over 2 EndFraction minus 10; when a = 40 Sam is 10 years old
StartFraction a Over 2 EndFraction + 10; when a = 40 Sam is 30 years old

Answers

GPT-4o mini
To express Sam's age based on his aunt's age, we need to follow the information given in the problem.

Sam is 10 years younger than one-half the age of his aunt. If we denote Sam's age as \( S \) and his aunt's age as \( a \), we can write the expression as:

\[
S = \frac{a}{2} - 10
\]

Now, we need to substitute \( a = 40 \) to find Sam's age:

\[
S = \frac{40}{2} - 10
\]
\[
S = 20 - 10
\]
\[
S = 10
\]

Given the choices, the correct algebraic expression that represents Sam's age is:

**StartFraction a Over 2 EndFraction minus 10; when a = 40 Sam is 10 years old.**

So the correct answer is:

**StartFraction a Over 2 EndFraction minus 10; when a = 40 Sam is 10 years old.**