Questions: An estate of 469,000 is left to three siblings. The eldest receives 6 times as much as the youngest. The middle receives 12,000 more than the youngest. How much does each receive? The eldest sibling received The middle sibling received The youngest sibling received

Solution Steps

To solve this problem, we need to set up equations based on the information given. Let \( y \) be the amount the youngest sibling receives. Then, the eldest receives \( 6y \), and the middle sibling receives \( y + 12,000 \). The sum of these amounts should equal the total estate of \$469,000. We can solve this equation to find the value of \( y \) and subsequently the amounts received by the other siblings.

Let \( y \) be the amount the youngest sibling receives. According to the problem, the eldest sibling receives 6 times as much as the youngest, so the eldest receives \( 6y \). The middle sibling receives \$12,000 more than the youngest, so the middle sibling receives \( y + 12,000 \).

The total estate is \$469,000. Therefore, the sum of the amounts received by all three siblings is: \[ y + 6y + (y + 12,000) = 469,000 \] Simplifying the equation, we have: \[ 8y + 12,000 = 469,000 \]

Subtract 12,000 from both sides: \[ 8y = 469,000 - 12,000 \] \[ 8y = 457,000 \] Divide both sides by 8 to solve for \( y \): \[ y = \frac{457,000}{8} = 57,125 \]

• The youngest sibling receives \( y = 57,125 \).
• The eldest sibling receives \( 6y = 6 \times 57,125 = 342,750 \).
• The middle sibling receives \( y + 12,000 = 57,125 + 12,000 = 69,125 \).

Final Answer