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
⇒ [tex]3y-5=x[/tex] - Carlos' age is 11 years higher than his brother's age
⇒ [tex]y+11=x[/tex]
We can solve for y, his brothers age, using substitution:
[tex]3y-5=y+11\\2y=16\\y=8[/tex]
Now, solve for x by substituting y in either of the equations:
[tex]y+11=x\\8+11=x\\x=19[/tex]
Therefore, Carlos is 19 years old.
Answer
Carlos is 19 years old.
