Question

7. The difference of Grandma Annie's age and twice Carl's is 22. Gran

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.