Chapter 13.4, Problem 52HP

To determine

To find: The amount of the greatest share.

Answer to Problem 52HP

  $\$20,000$ is the greatest share.

Explanation of Solution

Given information:

Three people are splitting $\$48,000$ using the ratio $5:4:3$ .

Let $x$ be the amount of each share.

Total number of shares $=5+4+3=12$

Total amount $=\$48,000$

Therefore,

Value of each share is

  $\begin{array}{l}12x=48,000\\ \Rightarrow \frac{12x}{12}=\frac{48000}{12}\\ \Rightarrow x=\frac{48000}{12}\\ \Rightarrow x=4000\end{array}$

Therefore,

Amount of first-person share is $5x$

  $\Rightarrow$ Amount of first-person share $=5\left(4000\right)$

  $\Rightarrow$ Amount of first-person share $=\$20,000$

Amount of second-person share is $4x$

  $\Rightarrow$ Amount of second-person share $=4\left(4000\right)$

  $\Rightarrow$ Amount of second-person share $=\$16,000$

Amount of third-person share is $3x$

  $\Rightarrow$ Amount of second-person share $=3\left(4000\right)$

  $\Rightarrow$ Amount of second-person share $=\$12,000$

Therefore,

On comparing we can say that

  $\$20,000$ is the greatest share.