Question

An inheritance is divided between 4 children as follows: André receives one-sixth of the inheritance plus $5,000, Bernard receives one-third of the inheritance minus $5,000, Caroline receives one-quarter of the inheritance minus $10,000 and Denise receives exactly one-third of the inheritance. What is the amount received by each child?

(Only Accurate answers)​

Answer 1

André received $9,000, Bernard received $3,000, Caroline received $2,000, and Denise received $8,000.

Explanation:

Let's call the total amount of the inheritance "x".

According to the problem:

André receives 1/6 of x + $5,000

Bernard receives 1/3 of x - $5,000

Caroline receives 1/4 of x - $10,000

Denise receives 1/3 of x

We can write an equation to represent the total inheritance:

x = (1/6)x + $5,000 + (1/3)x - $5,000 + (1/4)x - $10,000 + (1/3)x

Combining like terms, we get:

x = (7/12)x - $10,000

Bringing the "x" terms to one side and the constant terms to the other, we get:

(5/12)x = $10,000

Multiplying both sides by 12/5, we get:

x = $24,000

Now we can substitute this value back into the original equations to find out how much each child received:

André: (1/6)($24,000) + $5,000 = $9,000

Bernard: (1/3)($24,000) - $5,000 = $3,000

Caroline: (1/4)($24,000) - $10,000 = $2,000

Denise: (1/3)($24,000) = $8,000

Therefore, André received $9,000, Bernard received $3,000, Caroline received $2,000, and Denise received $8,000.