Question

1) (A% increase and B% decrease) You find a pair of shoes that have an original price of $145. Suppose the shoes are on sale for 15% off, and suppose there is also a sales tax of 8.5%. a) Calculate the total price you pay at the register if you first take 15% off, and then add on the 8.5% sales tax. Show all work clearly. b) Calculate the total price you pay at the register if you first add on the 8.5% sales tax, and then add in the 15% discount. Show all work clearly. c) In general, if you increase a number by A%, and also decrease the number by B%, does the order in which you perform the increase/decrease matter

Answer 1

The total price of of the shoes is $133.73.

The total price of the shoes if sales tax is added first is $133.73

Generally, it does not matter in which order the increase or decrease is performed.

What is the total price you would pay for the shoes?

A discount reduces the price of goods and services.

Price of the shoes after the discount = (100 - 15%) x $145

85% x $145

= 0.85 x $145

= 123.25

Taxes increase the price of goods and services.

Price of the shoes after the tax = (100 + 8.5%) x $123.25

108.5% x $123.25

1.085 x $123.25 = $133.73

What is the total price if sales tax is added first?

Price of the shoes after the tax = (100 + 8.5%) x $145

1.085 x $145 = $157.325

Price of the shoes after the discount = 0.85 x $157.325 = $133.73

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