Chapter 6.5, Problem 26IP

To determine

To find:List price of the television set.

Answer to Problem 26IP

List price of the television set $=\$349.5$

Explanation of Solution

Given information:

Selling price $=\$466$

Markup percent $=33\frac{1}{3}\%$ on list price or cost price.

We know

Selling price $=$ Cost price $+$ Markup

Given

Assume $\text{'}x\text{'}$ be the List price.

Markup is $33\frac{1}{3}\%$ of cost price

  $\begin{array}{l}33\frac{1}{3}=33+\frac{1}{3}\\ \Rightarrow 33\frac{1}{3}=\left(33\times \frac{3}{3}\right)+\frac{1}{3}\\ \Rightarrow 33\frac{1}{3}=\left(\frac{99}{3}\right)+\frac{1}{3}\\ \Rightarrow 33\frac{1}{3}=\frac{99+1}{3}\\ \Rightarrow 33\frac{1}{3}=\frac{100}{3}\end{array}$

Therefore

Markup percent $=33\frac{1}{3}\%=\frac{100}{3}\%$

Therefore,

Markup $=\left(\frac{\left(\frac{100}{3}\right)}{100}\right)\times x$

  $\Rightarrow$ Markup $=\left(\frac{100}{3\times 100}\right)\times x$

  $\Rightarrow$ Markup $=\frac{x}{3}$

Therefore,

Selling price $=$$x+\frac{x}{3}$

  $\Rightarrow$$466=x+\frac{x}{3}$

  $\Rightarrow$$466=\frac{3x+x}{3}$

  $\begin{array}{l}\Rightarrow 466=\frac{4x}{3}\\ \Rightarrow x=466\times \frac{3}{4}\\ \Rightarrow x=349.5\end{array}$

Therefore,

List price $=\$349.5$