Uncle Albert's estate is to be divided among his three nephews. The will specifies that Daniel receive one-half of the amount that Brain receives and that Raymond receive $1,000 less than one-third of the amount that Brain receives. If the estate amounts to $25,400 then how much does each inherit?
d = b/2
r = b/3 - 1000
d + b + r = 25400
b/2 + b + b/3 - 1000 = 25400
11b/6 = 26400
b = 14400
d = 7200
r = 3800
To solve the problem, let's break it down step by step:
Step 1: Determine the amount that Brain receives.
Let's denote the amount that Brain receives as "B".
Step 2: Calculate the amount that Daniel receives.
According to the will, Daniel receives one-half of the amount that Brain receives, which can be expressed as 0.5B.
Step 3: Calculate the amount that Raymond receives.
The will states that Raymond receives $1,000 less than one-third of the amount that Brain receives. So, the amount that Raymond receives can be expressed as 1/3B - $1,000.
Step 4: Write an equation for the total value of the estate.
The total value of the estate is given as $25,400, so we can write the equation: B + 0.5B + (1/3B - $1,000) = $25,400.
Step 5: Simplify and solve the equation for B.
Combining like terms, the equation becomes:
1B + 0.5B + (1/3B - $1,000) = $25,400
=> (6/6)B + (3/6)B + (2/6)B - $1,000 = $25,400
=> (11/6)B - $1,000 = $25,400.
Adding $1,000 to both sides of the equation gives:
(11/6)B = $26,400.
To solve for B, multiply both sides by the reciprocal of 11/6:
B = $26,400 * (6/11).
So, Brain receives B = $14,400.
Step 6: Calculate the inheritance for Daniel and Raymond.
Daniel receives half the amount that Brain receives: 0.5 * $14,400 = $7,200.
Raymond receives $1,000 less than one-third of the amount that Brain receives: (1/3) * $14,400 - $1,000 = $3,800.
Therefore, Daniel inherits $7,200, Raymond inherits $3,800, and Brain inherits $14,400.