15. Ben and Bill wins in the local lottery. They share their money in a ratio of 3: 4. Ben decided to give P400 to his little sister. The amount that Bill and Ben have now is in the ratio of 6: 7. Calculate the total amount of money Bill and Ben won.
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Let x be the total amount of money Bill and Ben won.
We know that the ratio of Ben's money to Bill's money is 3:4, so:
3/4 = x / (x-400)
We also know that the ratio of Ben's money (after giving P400 to his sister) to Bill's money is 6:7, so:
6/7 = (x-400) / x
We can use these two equations to solve for x.
First, cross-multiply the first equation:
4x = 3(x-400)
Then, cross-multiply the second equation:
7(x-400) = 6x
Now we can substitute the first equation into the second equation:
7(4x/3) = 6x
Simplifying this equation:
8x = 21x - 2800
13x = 2800
x = 21600
Therefore, the total amount of money Bill and Ben won is P21600.