Question

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?

A) 4x + 1
B) x + 4
C) 4x + 5
D) x + 16

Answer 1

The expression x + 4 represents how many years older the principal is than the teacher.

Step-by-step explanation:

Let x represent the student's age. The teacher's age is 6 years greater than 2 times the student's age, which can be represented by the expression 2x + 6. The principal's age is 10 years greater than 3 times the student's age, which can be represented by the expression 3x + 10. To find how many years older the principal is than the teacher, we subtract the teacher's age from the principal's age: (3x + 10) - (2x + 6).

Simplifying the expression, we get 3x + 10 - 2x - 6 = x + 4. Therefore, the expression x + 4 represents how many years older the principal is than the teacher.