Answer:
Paul's original share is £ 65
Step-by-step explanation:
Given,
The ratio of money Dan and Paul has = 11 : 5
Let, Dan's share = 11x,
Paul's share = 5x,
Where,
x is any positive real numbers,
Now, if Dan gives Paul £39 of his share,
Then, Dan's share = 11x - 39,
Paul's share = 5x + 39
Thus, the new ratio of there share = ![\frac{11x-39}{5x+39}](https://tex.z-dn.net/?f=%5Cfrac%7B11x-39%7D%7B5x%2B39%7D)
According to the question,
![\frac{11x-39}{5x+39}=\frac{1}{1}](https://tex.z-dn.net/?f=%5Cfrac%7B11x-39%7D%7B5x%2B39%7D%3D%5Cfrac%7B1%7D%7B1%7D)
By cross multiplication,
![11x - 39 = 5x + 39](https://tex.z-dn.net/?f=11x%20-%2039%20%3D%205x%20%2B%2039)
By additive property of equality,
![11x = 5x + 39 + 39](https://tex.z-dn.net/?f=11x%20%3D%205x%20%2B%2039%20%2B%2039)
By subtraction property of equality,
![11x - 5x = 78](https://tex.z-dn.net/?f=11x%20-%205x%20%3D%2078)
![6x = 78](https://tex.z-dn.net/?f=6x%20%3D%2078)
By division property of equality,
![x=\frac{78}{6}=13](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B78%7D%7B6%7D%3D13)
Hence, Paul's original share = 5(13) = £ 65