Question

An estate of $503,000 is left to three siblings. the eldest receives six times as much as the youngest. the middle sibling receives $14,000 more than the youngest. how much did each receive?

Answer 1

Let x, y, z, be the estate received to the eldest, middle, and youndest sibling, respectively.

The eldest sibling receives six times as much as youngest sibling,

`x=6z`

The middle sibling receives $14,000 more than the youngest,

`y=z+14000`

The total estate is worth $503000. So it follows that,

`\begin{gathered} x+y+z=503000 \\ 6z+(z+14000)+z=503000 \\ 8z=503000-14000 \\ 8z=489000 \\ z=61125 \end{gathered}`

Then the corresponding values of x, and y become,

`\begin{gathered} x=6(61125)=366750 \\ y=61125+14000=75125 \end{gathered}`

Thus, the estate received to the siblings are as follows,

`\begin{gathered} \text{Eldest}=366750\text{ dollars} \\ \text{Middle}=75125\text{ dollars} \\ \text{Youngest}=61125\text{ dollars} \end{gathered}`