Frank is 4 years older than Jimmie. 2 years ago Frank was 5 times as old as Jimmie. How old is Frank today?

Question

Help with word problem

 

Answer 1

When possible, use a variable to find the value the problem asks you to find.  Here,

   let x = Frank's age today

 

  "Frank is 4 years older than Jimmie"   means

      x    =  4         +         Jimmie's age

 

  "2 years ago Frank was 5 times as old as Jimmie"   means

         (  -2  +  x)      =    5   *    (Jimmie's age - 2)

 

Substitute x-4 (from first equation) in place of Jimmie's age in second equation:

       (x-2) = 5 * ( (x-4) -2 )

 

Proceed to solve:

      x - 2  = 5x -30

      -4x = -28

         x  =  7            Frank is 7 today.

 

Checking:

  Frank is 7.  Jimmie is 3.

  2 years ago, was (7-2) = 5*(3-2)   ?

                            5  =  5   ?   yes

Answer 2

Hi April!  This problem can be solved with two equations.  If F is Frank's age today and J is Jimmie's age today, then F-2 is Frank's age 2 years ago and J-2 is Jimmie's age 2 years ago.

 

So the problem tells us that:

 

F = J+4   -and-

F-2 = 5(J-2)

 

We can substitute the first equation into the second by replacing F with "J+4".  So the second equation looks like this:

 

J+4-2 = 5(J-2)

 

Simplifying both sides, we get

J+2 = 5J - 10

 

Subtracting J from both sides, we get

 

2 = 4J - 10

 

Adding 10 to both sides we get:

 

12 = 4J

 

Dividing both sides by 4, we get 

 

J=3

 

That's Jimmie's age today.  Franks age today is:

 

F = J + 4 = 3 + 4 = 7

 

So Frank's age today is 7 .

 

Hope that helps.  Let me know if it doesn't make sense or if you have any follow up questions!

 

Jeff

Answer 3

Equation 1: F=J+4

Equation 2: F-2=5(J-2)

Simplify Equation 2:

F-2=5J-10

F=5J-8

 

Substitute into Equation 1:

5J-8=J+4

4J=12

J=3 (Jimmie)

 

F=3+4 = 7 (Frank)