Answer:
Paul had £40 originally.
Step-by-step explanation:
Given
Let d be the money Dan has and p be the money Paul has
Then according to the given situation,
[tex]\frac{d}{p} = \frac{9}{5}\\d = \frac{9p}{5}\ \ \ Equation\ 1[/tex]
Now from the statement, "Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1"
[tex]\frac{d-32}{p} = 1[/tex] Eqn 2
From 2
[tex]d - 32 = p\\[/tex]
Putting d = 9p/5
[tex]\frac{9p}{5} - 32 = p\\9p - 160 = 5p\\9p-5p = 160\\4p = 160\\\frac{4p}{4} = \frac{160}{4}\\p = 40[/tex]
Checking
[tex]d = \frac{9(40)}{5} = \frac{360}{5} = 72\\\frac{d}{p} = \frac{72}{40} = \frac{9}{5}[/tex]
Hence,
Paul had £40 originally.
