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7. The difference of Grandma Annie's age and twice Carl's is 22. Gran
Annie's age is 13 less than 3 times Carl's. How old is Grandma Annie?

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theleangreenbean

Systems of Equations Word Problems

To solve these questions, we can translate key words into operations:

  • Difference = subtract
  • Twice = double
  • Less than = subtract

Solving the Question

We're given:

  • Difference of Annie's age and twice Carl's age is 22
  • Annie's age is 13 less than 3 times Carl's age

There are two variables given two us: Annie's age and Carl's age.

  • Let Annie's age be equal to x.
  • Let Carl's age be equal to y.

Translate the given information into two equations:

  • Difference of Annie's age and twice Carl's age is 22
    ⇒ [tex]x-2y=22[/tex]
  • Annie's age is 13 less than 3 times Carl's age
    ⇒ [tex]x=3y-13[/tex]

Now, we can substitute the fist equation into the second one to solve for y:

[tex](3y-13)-2y=22\\3y-13-2y=22\\y-13=22\\y=35[/tex]

Now, substitute y back into the second equation to solve for x:

[tex]x=3y-13\\x=3(35)-13\\x=105-13\\x=92[/tex]

Answer

Therefore, Grandma Annie is 92 years old.

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