A teacher's age is 6 years greater than 2 times a student's age. A principal's age is 10 years greater than 3 times the student's age. If x represents the student's age in years, which expression represents how many years older the principal is than the teacher?

Answer 1

Let's translate the information into algebraic expressions.

We have the student's age represented by x.

The teacher's age is 6 years greater than 2 times the student's age: \( 2x + 6 \).

The principal's age is 10 years greater than 3 times the student's age: \( 3x + 10 \).

Now, we need to determine how much older the principal is than the teacher. We can find this by subtracting the teacher's age from the principal's age:

\[ (3x + 10) - (2x + 6) \]

Let's simplify the expression:

\[ 3x + 10 - 2x - 6 \]
\[ (3x - 2x) + (10 - 6) \]
\[ x + 4 \]

So, the principal is \( x + 4 \) years older than the teacher.