John and Tom have $600 between them. If John gave Tom $50, then John would have twice as much as Tom. How much money does each have in the beginning?

Question

explanation, step by step and working out please.

Answer 1

John has  $x

Tom has 600 -x

 

After John giving  50 to Tom

 

John have = x-50

Tom have (600-x)+50=650 -x

 

x-50 =2(650 -x)

x -50 =1300 -2x

3x = 1350

x = 450

 

John has $x = $450
Tom has 600 -x = 600 -450 =$150

Answer 2

j + t = 600    equation 1

 

j-50 = 2(t + 50)

j - 50 = 2t + 100

j - 2t = 150   equation 2

 

From 1st equation t = 600-j

Substitute i to 2nd equation:

 

j - 2(600-j) = 150

j - 1200 + 2j = 150

3j = 1350

j = 450

 

t = 600-450 = 150

 

John had $450

Tom had $150