Chapter 6.5, Problem 37IP

To determine

To find:Are the selling prices of both stores are same.

Answer to Problem 37IP

Both selling prices are not same.

Explanation of Solution

Given information:

Regular price of a game system $=$ Original price $=\$299$

Discount amount $=\$75$

Sales tax $=7.5\%$ of discounted price.

Lassen Toys discounts first and then adds Tax.

Pineapple systems adds the tax first and then takes the discount.

We know

Discounted price $=$ Original price $-$ Discount amount

Given

Original price $=\$299$

Discount amount $=\$75$

Discounted price $=$$\$299-\$75$

  $\Rightarrow$ Discounted price $=$$\$224$

We know

Sales tax $=7.5\%$ of discounted price

Selling price = Discounted price $+$ Sales tax

  $\Rightarrow$ Selling price = $224+\left(\frac{7.5}{100}\right)\times 224$

  $\Rightarrow$ Selling price = $224+\left(0.075\right)\times 224$

  $\Rightarrow$ Selling price = $224+16.8$

  $\Rightarrow$ Selling price = $\$240.8$

Therefore,

Selling price in Lassen toys store is $\$240.8$

Given

Pineapple systems adds the tax first and takes the discount.

We know

Sales tax $=7.5\%$ of Original price

  $\Rightarrow$ Sales tax $=\left(\frac{7.5}{100}\right)\times 299$

  $\Rightarrow$ Sales tax $=\left(0.075\right)\times 299$

  $\Rightarrow$ Sales tax $=\$22.425$

Selling price without discount $=$ Original price $+$ Sales tax

  $\Rightarrow$ Selling price without discount $=$$\$299+\$22.425$

  $\Rightarrow$ Selling price without discount $=$$\$321.425$

Selling price =Selling price without discount $-$ Discount amount

  $\Rightarrow$ Selling price = $321.425-75$

  $\Rightarrow$ Selling price = $\$246.425$

Therefore,

Selling price in Pineapple systems store is $\$246.425$

We got

Selling price in Pineapple systems store is $\$246.425$

Selling price in Lassen toys store is $\$240.8$

On comparing we can say that both selling prices are not same.