How many pencils does each student have?

Question

If jack give one of his pencils to kim, each student will have the same number of pencils. If kim gives jack one of her pencils, jack will have twice as many as kim. How many pencils does each student have?

Answer 1

Let:

  J = number of pencils Jack starts with

  k = number of pencils Kim starts with

 

Translate:

  "If jack give one of his pencils to kim, each student will have the same number of pencils"

      means     J-1 = K+1   

 

  "If kim gives jack one of her pencils, jack will have twice as many as kim"

     means    2*(K-1) = (J+1) 

 

The math:

    J-1=K+1

    J = K+2             [add 1 to both sides to solve for J]

Substitute that into the second equation:

     2*(K-1) = ((K+2)+1)

     2K - 2   =  K + 3

        2K  = K + 5              [add 2 to both sides]

         K = 5                 [subtract K from both sides]

Plug that into either equation to solve for J  [eq1 is easier]:

       J - 1 = K + 1

       J - 1 = 5 + 1

       J - 1 = 6

        J = 7

 

Checking (very important):

  If Jack gave one of his 7 pencils to Kim (who has 5), each would have 6 pencils.

  If Kim gave on her 5 pencils to Jack (who has 7), Jack would have 8, which is twice the 4 that Kim would have.