If €8200 is divided among A,B and B so that A's share is 2/5 of B's and B's is 3/4 of C's share, how much does C's get?
A = 2/3 b
b = 3/4 c
a+b+c = 8200
Now just solve for c.
Mathematics
Let's break down the information given step-by-step to find the answer.
Step 1: Determine the share of A relative to B.
A's share is given as 2/5 of B's. We can represent this as:
A's share = (2/5) * B's share
Step 2: Determine the share of B relative to C.
B's share is given as 3/4 of C's share. We can represent this as:
B's share = (3/4) * C's share
Step 3: Calculate the total amount given to A, B, and C.
The total amount given is €8200. Therefore, we have:
A's share + B's share + C's share = €8200
Step 4: Substitute the values from Step 1 and Step 2 into Step 3.
We can substitute the expressions from Step 1 and Step 2 into the equation from Step 3. This gives us:
(2/5) * B's share + (3/4) * C's share + C's share = €8200
Step 5: Simplify the equation.
To simplify the equation, let's factor out C's share:
(3/4 + 1) * C's share + (2/5) * B's share = €8200
(7/4) * C's share + (2/5) * B's share = €8200
Step 6: Solve the equation.
We need additional information to solve the equation. The given information does not allow us to determine the exact values of A, B, and C.
Therefore, without additional information, we cannot determine the amount C gets.
To solve this problem, we'll break it down step by step.
Let's assume that C's share is represented by the variable "x."
From the given information, we know that B's share is 3/4 of C's share. So, B's share is (3/4)*x.
We're also given that A's share is 2/5 of B's share. Therefore, A's share is (2/5)*(3/4)*x.
Now, we can sum up all the shares to equal the total amount of €8200:
A's share + B's share + C's share = €8200
Substituting the expressions we derived:
(2/5)*(3/4)*x + (3/4)*x + x = €8200
Simplifying the equation:
(6/20)*x + (12/20)*x + x = €8200
(18/20)*x + (12/20)*x + x = €8200
(30/20)*x = €8200
(3/2)*x = €8200
3x = 2 * €8200
3x = €16400
Now, we can solve for x, which represents C's share:
x = €16400 / 3
By dividing €16400 by 3, we find that C's share is approximately €5466.67.