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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?

 Jan 19, 2019
 #1
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+1

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.

 Jan 19, 2019
 #2
avatar+107405 
+1

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

 

 

 

cool cool  cool

 Jan 19, 2019

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