Question

The expression 1.08(0.85p) represents the total amount Austin paid for a jacket originally priced p dollars. Which changes to the original price could have resulted in this expression?

Answer 1

Given the expression:

$\text{ 1.08(0.85p)}$

Let's interpret,

a.) 0.85p

- Knowing that p represents the original price of the jacket, 0.85 represents the remaining price of the jacket after a discount. The difference between 1 and 0.85 is the discount.

We get,

$\text{ 1 - 0.85 = 0.15 }\rightarrow\text{ 0.15 x 100 = 15\%}$

Multiplied by 100, the discount is therefore 15%.

b.) 1.08(0.85p)

- The 1.08 in the expression represents the factor after a sales tax, the difference between 1 and 1.08 is the sales tax.

We get,

$\text{ 1.08 - 1 = 0.08 }\rightarrow\text{ 0.08 x 100 = 8\%}$

Multiplied by 100, the sales tax is therefore 8%.

Conclusion:

The changes to the original price are a Sales tax of 8% and then a discount of 15%.