Question

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?

Answer 1

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
  ⇒
  `x-2y=22`

• Annie's age is 13 less than 3 times Carl's age
  ⇒
  `x=3y-13`

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

`(3y-13)-2y=22\\3y-13-2y=22\\y-13=22\\y=35`

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

`x=3y-13\\x=3(35)-13\\x=105-13\\x=92`

Answer

Therefore, Grandma Annie is 92 years old.