Question

Dan and Paul share some money in the ratio 9:5.

Answer 1

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,

$\frac{d}{p} = \frac{9}{5}\\d = \frac{9p}{5}\ \ \ Equation\ 1$

Now from the statement, "Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1"

$\frac{d-32}{p} = 1$     Eqn 2

From 2

$d - 32 = p$

Putting d = 9p/5

$\frac{9p}{5} - 32 = p\\9p - 160 = 5p\\9p-5p = 160\\4p = 160\\\frac{4p}{4} = \frac{160}{4}\\p = 40$

Checking

$d = \frac{9(40)}{5} = \frac{360}{5} = 72\\\frac{d}{p} = \frac{72}{40} = \frac{9}{5}$

Hence,

Paul had £40 originally.