Question 1097900


the problem states:


Andrew has more money than Ben, if Andrew gave Ben £20, they would have the same amount, while if Ben gave Andrew £22, Andrew would have then have twice as much as Ben. 


Andrew has more money than Ben leads to:


A > B.


if Andrew gave Ben 20, they would have the same amount leads to:


A - 20 = B + 20


if Ben gave Andrew 22, Andrew would have twice as much as Ben leads to:


A + 22 = 2 * (B - 22).


you have:


A - 20 = B + 20
A + 22 = 2 * (B - 22)


simplify to get:


A - 20 = B + 20
A + 22 = 2B - 44


get all the A's and B's on the same side of the equation and you get:


A - B = 40
A - 2B = -66


subtract the second equation from the first and you get:


B = 106


use either of the first two original equations to find the value of A.


i used the second one.


A + 22 = 2 * (B - 22)
when B = 106, this becomes A + 22 = 2 * (106 - 22).
subtract 22 from both side and simplify to get A = 146.


you have A = 146 and B = 106


evaluate both original equations to see if they hold true with these values for A and B.


A - 20 = B + 20 becomes 146 - 20 = B + 20 which becomes 126 = 146 which is true.


A + 22 = 2 * (B - 22) becomes 146 + 22 = 2 * (106 - 22) which becomes 168 = 2 * (84) which becomes 168 = 168 which is true.


the values for A and B are good.


your solution is that A = 146 and B = 106.