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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
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
