Question 1097900: 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.
So, new working
A-20 = B+20
B-22 =2A +22
Solve for one, substitute new value into other equation. I "solved" equation 2, and got:
B=2A+44
substituting it into equation 1:
A-20=2A+44+20
A=2A+84
A=84
I ended up with a result of 84 (wrong)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
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.
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