Q:

Teresa’s age is 5 years more than twice Ben’s age. If Ben is x years old, the expression _____ gives the sum of Ben’s and Teresa’s ages. If Ben is 7 years old, the sum of Ben’s and Teresa’s ages is _____ years.

Accepted Solution

A:
Using a system of equations, it is found that:If Ben is x years old, the expression 3x + 5 gives the sum of Ben’s and Teresa’s ages. If Ben is 7 years old, the sum of Ben’s and Teresa’s ages is 26 years.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.In this problem, the variables are given by:Variable x: Ben's age.Variable y: Teresa's age.Teresa’s age is 5 years more than twice Ben’s age, hence:y = 2x + 5The sum of their ages is:x + y = x + 2x + 5 = 3x + 5.Ben is 7 years old, hence the sum is given by:3(7) + 5 = 26.Then:If Ben is x years old, the expression 3x + 5 gives the sum of Ben’s and Teresa’s ages. If Ben is 7 years old, the sum of Ben’s and Teresa’s ages is 26 years.More can be learned about a system of equations at