Chapter 6.5, Problem 27IP

To determine

To find:The Original price of each item and complete the table

Answer to Problem 27IP

Marked-down price	$\$2.99$	$\$4.99$	$\$6.99$	$\$8.99$	$\$10.99$
Original price	$\$3.74$	$\$6.24$	$\$8.74$	$\$11.24$	$\$13.74$

Explanation of Solution

Given information:

Mark-down percent for all items $=20\%$ of Original price

Given table containing Selling prices of several items.

We know

Selling price $=$ Original price $-$ Markdown

Given

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

Markup is $20\%$ of Original price

Therefore,

Markup $=\left(\frac{20}{100}\right)\times x$

  $\Rightarrow$ Markup $=\left(0.2\right)\times x$

  $\Rightarrow$ Markup $=0.2x$

Therefore,

Selling price $=$$x-0.2x$

  $\Rightarrow$ Selling price $=0.8x$

If Selling price that is markdown price $=\$2.99$

We get

  $\begin{array}{l}\Rightarrow 2.99=0.8x\\ \Rightarrow x=\frac{2.99}{0.8}\\ \Rightarrow x=3.7375\end{array}$

To nearest cent, Original price $=\$3.74$

Therefore,

For Markdown price $=\$2.99$ ,Original price $\$3.74$

If Selling price that is markdown price $=\$4.99$

We get

  $\begin{array}{l}\Rightarrow 4.99=0.8x\\ \Rightarrow x=\frac{4.99}{0.8}\\ \Rightarrow x=6.2375\end{array}$

To nearest cent, Original price $=\$6.24$

Therefore,

For Markdown price $=\$4.99$ ,Original price $\$6.24$

If Selling price that is markdown price $=\$6.99$

We get

  $\begin{array}{l}\Rightarrow 6.99=0.8x\\ \Rightarrow x=\frac{6.99}{0.8}\\ \Rightarrow x=8.7375\end{array}$

To nearest cent, Original price $=\$8.74$

Therefore,

For Markdown price $=\$6.99$ ,Original price $\$8.74$

If Selling price that is markdown price $=\$8.99$

We get

  $\begin{array}{l}\Rightarrow 8.99=0.8x\\ \Rightarrow x=\frac{8.99}{0.8}\\ \Rightarrow x=11.2375\end{array}$

To nearest cent, Original price $=\$11.24$

Therefore,

For Markdown price $=\$8.99$ ,Original price $\$11.24$

If Selling price that is markdown price $=\$10.99$

We get

  $\begin{array}{l}\Rightarrow 10.99=0.8x\\ \Rightarrow x=\frac{10.99}{0.8}\\ \Rightarrow x=13.7375\end{array}$

To nearest cent, Original price $=\$13.74$

Therefore,

For Markdown price $=\$10.99$ ,Original price $\$13.74$