Original price

​If the original price of an item is x...

​The discount is a part of x.

​

(discount rate)(original price)=amount of discount

​

The sale price is found by subtracting the amount of the discount from the original price.

​

​Sale price= original price - amount of discount

​p = x - (%)x

Multiple Choice

To find the amount of discount...

• Multiply the discount rate and the original.

• Divide the discount rate and the original.

• Subtract the discount rate from the original.

• Multiply the original and the sale price.

Multiple Choice

To find the sale price...

• Subtract the discount from the original.

• Subtract the discount rate from the original.

• Multiply the discount rate and the original.

• Subtract the sale price from the discount rate.

​Example

​Sally paid $42.50 for a item that was on sale for 15% off. Find the original price.

​Let x = original price.

​Sale price= original price - discount

p= ​​x - (%)x

​​p=x-15%x

​p=x-0.15x

​p=0.85x

​

​

​Continued on next slide.

​Example

Multiple Choice

The Sandersons bought a new couch on sale for  20% off. They paid $900. Which equation could be used to find the original price?

• $$900=0.8x$$

• $$900=1.2x$$

• $$900=0.2x$$

• $$900-0.2x=100$$

Multiple Choice

The Sandersons bought a new couch on sale for  20% off. They paid $900. What ist he original price?

• $1080

• $920

• $1125

• $720

​If the original price of an item is x...

​The tax is a part of x.

​

(tax rate)(original price)=amount of tax

​

The new price is found by adding the amount of the tax to the original price.

​

​Final price= original price + tax amount

​Algebraically

​​The tax is a part of x.

​(tax rate)original price)=amount of tax

​

The price is found by adding the amount of the tax to the original price.

​

​Price= original price + tax

p= ​​x + (%)x

​Example

​Sally paid $42.50 for a item, including a 6% sales tax. FInd the original price.

​

Let x = original price.

Total price= original price + tax

p= ​​x + %x

​​p=x+6%x

​p=x+0.06x

​p=1.06x

​

​continued on next slide

​Example

Multiple Choice

The sales tax where Mary lives is 7.5%.  Mary paid a total 0f $47.30? Which equation would find the price before tax??

• 47.30=(1.075)x

• 47.30=(1.75)x

• 47.30=(0.075)x

• 47.30=1.075

Multiple Choice

A couple buys a house for a total price of $319,000. If the total price includes a 6.75% sales tax. Which equation could be used to find the cost of the house before taxes?

• 319000=0.0675x

• 319000=0.9325x

• 319000=1.0675x

• 319000=1675x

Fill in the Blanks

After a 7.5% tax is applied, a meal at a restaurant ends up costing $51.94.

What was the cost of the meal without the tax?