A sum of money is divided between three men x y and z in ratio of 5:3:1 if y has 700 more than z calculate how much x has
Let's assume that the amount of money that z has is represented by the variable 'm'.
According to the given ratio, y has 700 more than z, which means that y has m + 700.
The ratio between x, y, and z is 5:3:1.
So, the total ratio is 5 + 3 + 1 = 9.
To find out how much x has, we need to calculate the fraction of the total amount that belongs to x.
This fraction is represented by 5/9.
Therefore, the amount of money that x has can be calculated as (5/9) * Total Amount.
The remaining amount can be calculated as the difference between the total amount and the sum of the amounts of y and z.
So, (5/9) * Total Amount = Total Amount - (m + m + 700).
Simplifying this equation, we get:
5 * Total Amount = 9 * Total Amount - (2m + 700).
Rearranging the equation, we get:
4 * Total Amount = 2m + 700.
Dividing both sides of the equation by 4, we get:
Total Amount = (2m + 700) / 4.
Since we know that y has m + 700, we can substitute this value into the equation:
Total Amount = (2(m + 700) + 700) / 4.
Simplifying this equation, we get:
Total Amount = (2m + 1400 + 700) / 4.
Total Amount = (2m + 2100) / 4.
Now, let's find the value of x.
x = (5/9) * Total Amount.
Substituting the value of Total Amount, we get:
x = (5/9) * (2m + 2100) / 4.
Simplifying this equation, we get:
x = (10m + 10500) / 36.
So, x has an amount of (10m + 10500) / 36.