A sum of money is shared among three brothers. The eldest received 7/13 of it and the second brother receives 2/3 of the remainder. If the youngest brother receives $200, find the sum of money shared.
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Let's solve this step-by-step.
Step 1: Let's call the total sum of money shared as "x".
Step 2: The eldest brother received 7/13 of the total amount, which can be written as (7/13) * x.
Step 3: The remainder after the eldest brother receives his portion can be calculated as (x - (7/13) * x) = (6/13) * x.
Step 4: The second brother receives 2/3 of the remainder, which can be written as (2/3) * ((6/13) * x).
Step 5: We know that the youngest brother receives $200. So, we can set up the equation:
(2/3) * ((6/13) * x) = $200.
Step 6: To find the value of x, let's solve this equation:
(2/3) * ((6/13) * x) = $200.
Multiplying both sides by (3/2), we get:
(6/13) * x = $300.
Step 7: To find the value of x, let's isolate x by multiplying both sides by (13/6):
x = ($300) * (13/6).
Simplifying, we get:
x = $650.
Therefore, the sum of money shared among the three brothers is $650.
To find the sum of money shared among the three brothers, we need to work backwards from the given information.
Let's start by finding the amount of money the second brother received. We know that the eldest brother received 7/13 of the total sum. So, the remainder of the money left after the eldest brother received his share is (1 - 7/13).
The second brother then receives 2/3 of this remainder. So, the amount received by the second brother can be calculated as ((1 - 7/13) * (2/3)).
Now, we can find the total sum of money shared by adding the amounts received by each brother. We know that the sum of money received by the three brothers is equal to the amount received by the youngest brother plus the amount received by the second brother plus the amount received by the eldest brother.
Given that the youngest brother received $200, we can set up the equation as follows:
Total sum = Amount received by the youngest brother + Amount received by the second brother + Amount received by the eldest brother
Total sum = 200 + ((1 - 7/13) * (2/3)) + (7/13)
By calculating this expression, we can determine the sum of money shared among the three brothers.
eldest gets = 7 x/13
second gets = 2 (x-7x/13)/3 =( 2/3) ( 6x/13) = 4 x/13
third = 200 = x - 7 x/13 - 4 x/13 = 13 x/13 - 11 x/13 = 2 x/13
x = 1300