Word Problem

Question

Timothy's age in 3 years will be twice what it was 11 years ago. How old is Timothy now

Answer 1

First we must figure out what the word problem is telling us. It is saying that timothy current age which we will name x plus 3 years will equal twice of 11 years before today.

 

So our equation looks like this

 

x + 3 = 2(x-11)

 Distribute the two

 

x + 3 = 2x - 22

Now get x on one side and everything that is not x on another side.

you end up with

 

25_years = x

 

Before  we claim that this is the age let us see if the age works for both sides of the equation.

x + 3

25 + 3 = 28

 

2(x-11)

2(25 - 11) = 2(14) = 28

 

Since it works, we can now say with confidence that timothy is 25 years old

 

 

Answer 2

"How old is Timothy now?"   When practical, define a variable for the value the problem asks you to find (so you won't forget to solve for it at the end).

 

Let x= Timothy's age now

 

Translate:

 

  "Timothy's age in 3 years will be twice what it was 11 years ago"   means

       (    x           +     3 )       =      2          *         (  x - 11)

 

The math:

    x + 3 = 2(x-11)

    x + 3 = 2x - 22             [distribute]

    x + 25 = 2x                  [add 22 to both sides]

      25 = x                     [subtract 25 from both sides]

Timothy is 25.

 

Check:

   Is   (25+3) = 2*(25-11)   ?

          28 = 50-22   ?

          28 = 28   ?yes

 

Answer 3

Let Tim's age = x

 

11 years ago, his age was x - 11

 

Three years from now, his age will be x + 3

 

We know that

 

(x + 3) = 2(x - 11)

 

x + 3 = 2x - 22

 

3 = x - 22

 

x = 25. Timothy is 25 years old