Chapter 6.5, Problem 40HP

To determine

To find:Selling price of dress and percent of Discount.

Answer to Problem 40HP

Selling price of dress $=\$71.744535$

Discount $=52.17\%$

Explanation of Solution

Given information:

Original price of item $=\$150$

Mark down $=10\%$ each week until item sale.

Given

Original price of item $=\$150$

Mark down $=10\%$ each week until item sale.

Markdown price after first week $=$ Original price $-$ Markdown amount

  $\Rightarrow$ Markdown price after first week $=150-\left(\frac{10}{100}\right)150$

  $\Rightarrow$ Markdown price after first week $=150-\left(0.1\right)150$

  $\Rightarrow$ Markdown price after first week $=150\left(0.9\right)$

Markdown price after second week = Markdown price after first week $-$

  $10\%$ of Markdown price after first week

  $\Rightarrow$ Markdown price after second week $=150\left(0.9\right)-\left(\frac{10}{100}\right)150\left(0.9\right)$

  $\Rightarrow$ Markdown price after second week $=150\left(0.9\right)-\left(0.1\right)150\left(0.9\right)$

  $\Rightarrow$ Markdown price after second week $=150\left(0.9\right)\left(0.9\right)$

  $\Rightarrow$ Markdown price after second week $=150{\left(0.9\right)}^2$

Markdown price after third week = Markdown price after second week $-$

  $10\%$ of Markdown price after second week

  $\Rightarrow$ Markdown price after third week $=150{\left(0.9\right)}^2-\left(\frac{10}{100}\right)150{\left(0.9\right)}^2$

  $\Rightarrow$ Markdown price after third week $=150{\left(0.9\right)}^2-\left(0.1\right)150{\left(0.9\right)}^2$

  $\Rightarrow$ Markdown price after third week $=150{\left(0.9\right)}^3$

We got

Markdown price after first week $=150\left(0.9\right)$

Markdown price after second week $=150{\left(0.9\right)}^2$

Markdown price after third week $=150{\left(0.9\right)}^3$

On comparing, we can conclude that

Markdown price after $n^{th}$ week $=150{\left(0.9\right)}^n$

Given item sells during seventh week

So, substitute $n=7$

We get

  $\Rightarrow$ Markdown price after seventh week $=150{\left(0.9\right)}^7$

  $\Rightarrow$ Markdown price after seventh week $=150\left(0.4782969\right)$

  $\Rightarrow$ Selling price $=$ Markdown price after seventh week $=\$71.744535$

We got

Original price $=O$$=\$150$

Selling price of dress $=\$71.744535$

Amount of change $=A=$ Selling price $-$ Original price

  $\Rightarrow$$A=$$\$71.744535-\$150$

  $\Rightarrow$$A$$=\$78.255465$

Percent of change $=\frac{A}{O}\times 100$

  $\Rightarrow$ Percent of change $=\frac{-78.255465}{150}\times 100$

  $\Rightarrow$ Percent of change $=\left(-0.5217031\right)\times 100$

  $\Rightarrow$ Percent of change $=-52.17\%$

Therefore,

Percent of change $=52.17\%$ and negative sign indicates Discount.

  $\Rightarrow$ Discount $=52.17\%$