A sum of money is shared among three brothers. The eldest receives 7/13 of it and the 13 next receives 2/3 of the remainder. If the youngest brother receives $6, find the sum of money shared.
13/13 x - 7/13 x = 6/13 x
2/3 * 6/13 x---> brother two
1/3 * 6/13 x --->brother 3 = 6
so
2/13 x = 6
x = 3*13 = 39
To find the sum of money shared among the three brothers, we will work backwards using the information given in the question.
Let's start by finding out how much money the middle brother receives. According to the question, the eldest brother receives 7/13 of the total amount. This means that the remainder, which is not received by the eldest brother, is 6/13 of the total amount.
Next, we are told that the middle brother receives 2/3 of the remainder. So, we can calculate the middle brother's share by multiplying 2/3 by the remainder:
Middle brother's share = (2/3) × (6/13) of the total amount
Now, let's determine the amount that is left for the youngest brother. We know that the youngest brother receives $6, which is equal to 1/3 of the total remainder. Therefore, we can find the total remainder by multiplying $6 by 3:
Total remainder = $6 × 3 = $18
Since the youngest brother's share is $6, the total amount shared among the three brothers is the sum of the youngest brother's share plus the total remainder:
Total amount shared = youngest brother's share + total remainder
Total amount shared = $6 + $18
Total amount shared = $24
Therefore, the sum of money shared among the three brothers is $24.