Make an equation for the following:

Question

John and Kayla both reach into a bowl of diamonds and pull some out, if John gives Kayla a diamond, she will have twice as many as him, and if Kayla gives one to John, they will have the same amount as each other. How many diamonds did they take?

Answer 1

Let j represent John's diamonds

and k represent Kayla's diamonds

 

2(j-1)= k+ 1   Since, John gave one, he will be left with one less and

Kayla will have one more. Multiply John's diamonds by 2 because Kayla will have twice as much, given.

  j + 1=  k -1   Since, Kayla gave one, she will be left with one less and 

John will have one more. These are equal quantities, given.

Now solve,

2j -2 = k+ 1

  j +1= k - 1    Rewrite and solve for j, j = k - 2

 

2j - k = 3

2(k - 2) - k = 3  Plug in (k-2) for j.

2k - 4 - k = 3

k = 7

j  = 7-2

j  = 5

 

Solution: Kayla has 7 and John has 5 diamonds.

 

 

Answer 2

Let:

• J = the number  of diamonds that John has
• K = the number of diamonds that Kayla has

 

If John gives Kayla a diamond, she will have twice as many as him:

 

      J-1 = (1/2)(K+1)

 

If Kayla gives one to John, they will have the same amount as each other:

 

      K-1 = J+1

     So K = J+2

 

Substitute J+2 in place of K in the first equation:

 

      J-1 = (1/2)(K+1)

      2(J-1) = K+1

     2J-2 = J+2+1

      J = 5

 

John picks 5 diamonds.  Kayla has K = J+2 = 5+2 = 7 diamonds