julie5924
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Carlos is 5 less than 3 times his brother's age. Carlos' age is also 11 years older than his brother's age. How old is Carlos?​

Sagot :

theleangreenbean

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.

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