Please Help Explain

Question

After being discounted 10%, a weather radio sells for $80.96. Find the original price.

Answer 1

The discount lowers the original price by 10 %

Original price = 100 % of the cost

Discount price = (100% - 10%) = 90% of the cost, the Original Price

We know the discount price = 80.96 and represents 90% of the Original Price

Then

80.96 = .90(Original Price)

Divide both sides of the equation by 0.90 to find the Original Price

80.96/0.90 = Original Price

89.96 = Original Price to the nearest cent.

Checking

89.96 * .90 = 80.96 or the Discount Price to the nearest cent.

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Answer 2

Original price = P = $89.84

P-P/10 = 80.96 1/10 is 10%

9P/10 = 80.96 P-P/10 is 9P/10 1-1/10=9/10

9P = 809.6 Multiply both sides by 10, then divide both by 9

P = 809.6/9 = 89.8444... or round off to $89.84, close to $90

Rough check of the answer:

Discounted price is close to $81 Take 10% of $90 = $9 Subtract $9 from $90 to get $81

$89.84 is very close to $90 and is $90 rounded off to the nearest dollar.