The total cost of a new calculator is

$81.05. This price includes a 10% student

discount. Followed by a 6.5% sales tax.

What was the original price of the

calculator, not including the tax or the

discount?

This question bus incomplete because it lacks the appropriate options.

Complete Question

The total cost of a new calculator is

$81.05. This price includes a 10% student discount. Followed by a 6.5% sales tax. What was the original price of the calculator, not including the tax or the discount?

A. $77.69

B. $83.99

C. $78.80

D. $84.56

Answer:

D. $84.56

Step-by-step explanation:

From the question, we are given the following values

Total cost of a new calculator = $81.05

Student discount = 10%

Sales tax = 6.5%

The formula to use is

Total price = Original price (1 ± r)

Where r = rate of the discount or sales tax

Step 1

Find the original price of the calculator without the discount

Because we are calculating using discount we are using the minus sign

Total price = $81.05

r = 10% = 0.1

Total price = Original price (1 - r)

$81.05 = Original price (1 - 0.1)

$81.05 = Original Price * 0.9

Original price = $81.05: 0.9

= $90.055555556

Approximately, the original price without the 10% discount is $90.06

Step 2

Find the Original price without the sales tax

Because we are calculating using sales tax we are using the plus sign

Total price = $90.06

This is because the Original price without the discount = Current total price with sales tax for step 2

r = 6.5% = 0.065

Total price = Original price (1 + r)

$90.06 = Original price (1 + 0.065)

$90.06 = Original Price * 1.065

Original price = $90.06: 1.065

= $84.563380282

Approximately, the original price without the 10% discount and 6.5% sales tax is $84.56