Dan and Paul share some money in the ratio 13:5.
Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1.
How much did Paul originally have?
D/P =13/5,
(D-32)/(P+32) =1, solve for D, P
D = 104 pounds - what Dan originally had
P = 40 pounds -what Paul originally had
104 - 32 =72 - what Dan has after giving Paul 32 P.
40 + 32 =72 - what Paul has after receiving 32 P.
+130085 Let total amount = T
So
Dan originally has (13/18)T and Paul has (5/18)T
So....after Dan gives Paul 32 pounds....we have that
(13/18)T - 32 = (5/18)T + 32 simplify
(13/18)T - (5/18)T = 64
(8/18)T = 64
(4/9)T = 64
T = 64 (9/4) = 144
So... Paul originally had (5/18)(144) = 40 pounds
