Systems of Equations Word Problems
To solve these questions, we can translate key words into operations.
- Older = add
- Less than = subtract
Solving the Question
We're given:
- Carlos' age is 5 less than 3 times his brother's age
- Carlos' age is 11 years higher than his brother's age
There are two variables present in this problem: Carlos' age and his brother's age.
- Let Carlos' age equal x
- Let his brother's age equal y
Translate the given information into equations:
- Carlos' age is 5 less than 3 times his brother's age
⇒

- Carlos' age is 11 years higher than his brother's age
⇒

We can solve for y, his brothers age, using substitution:

Now, solve for x by substituting y in either of the equations:

Therefore, Carlos is 19 years old.
Answer
Carlos is 19 years old.