Chapter 6.5, Problem 38IP

To determine

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

Answer to Problem 38IP

Both selling prices are same.

Explanation of Solution

Given information:

Regular price of a game system $=$ Original price $=\$195$

Discount $=35\%$

Sales tax $=6.75\%$

Calby electronics discounts first and then adds Tax.

Game zinger adds the tax first and then takes the discount.

We know

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

Given

Original price $=\$195$

Discount $=35\%$ of Original price

Discount amount $=\left(\frac{35}{100}\right)\times 195$

  $\Rightarrow$ Discount amount $=\left(0.35\right)\times 195$

  $\Rightarrow$ Discount amount $=68.25$

Therefore,

Discounted price $=$$\$195-\$68.25$

  $\Rightarrow$ Discounted price $=$$\$126.75$

We know

Sales tax $=6.75\%$ of discounted price

Selling price = Discounted price $+$ Sales tax

  $\Rightarrow$ Selling price = $126.75+\left(\frac{6.75}{100}\right)\times 126.75$

  $\Rightarrow$ Selling price = $126.75+\left(0.0675\right)126.75$

  $\Rightarrow$ Selling price = $126.75+8.556$

  $\Rightarrow$ Selling price = $\$135.306$

Therefore,

Selling price in Calby electronics store is $\$135.306$

Given

Game zinger adds the tax first and takes the discount.

We know

Sales tax $=6.75\%$ of Original price

  $\Rightarrow$ Sales tax $=\left(\frac{6.75}{100}\right)\times 195$

  $\Rightarrow$ Sales tax $=\left(0.0675\right)\times 195$

  $\Rightarrow$ Sales tax $=\$13.1625$

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

  $\Rightarrow$ Selling price without discount $=$$\$195+\$13.1625$

  $\Rightarrow$ Selling price without discount $=$$\$208.1625$

Given

Discount $=35\%$ of selling price without discount

  $\Rightarrow$ Discount amount $=\left(\frac{35}{100}\right)\times 208.1625$

  $\Rightarrow$ Discount amount $=\left(0.35\right)\times 208.1625$

  $\Rightarrow$ Discount amount $=\$72.857$

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

  $\Rightarrow$ Selling price = $\$208.1625-\$72.857$

  $\Rightarrow$ Selling price = $\$135.306$

Therefore,

Selling price in Game zinger store is $\$135.306$

We got

Selling price in Calbyelectronics store is $\$135.306$

Selling price in Game zinger store is $\$135.306$

On comparing we can say that both selling prices are same.