bob and tom love balls. bob wants 8 of toms balls so he can have twice as many. tom want 8 of bob balls so he can have the same number. How many balls did each

Question

bob and tom love balls. bob wants 8 of toms balls so he can have twice as many. tom want 8 of bob balls so he can have the same number. How many balls did each have before swap

Answer 1

Let B = the number of balls Bob has

Let T = the number of balls Tom has

 

B - 8 = T + 8

B + 8 = 2 ( T - 8) rewrite this equation as B + 8 = 2 T - 16 now solve the system of two equations:

 

B - 8 = T + 8

B + 8 = 2T -16   add these two equations: 

2B + 0 = 3T - 8 solve for B

B = 3/2T - 4 now substitute B in equation above B - 8 = T +8

3/2 T - 4 -8 = T + 8 solve for T or number of Tom's balls.

3/2T  -12 = T + 8 simplify

3/2T = T + 20 multiply both sides by 2

3T = 2T + 40

T = 40  and B = 56

Put 40 in one of the equations to solve for B. 

 

Both T and B satisfy both conditions 

Take away 8 balls from Bob's number and add 8 balls to Tom's number and they are equal!!