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A discounted amusement park ticket costs $12.95 less than the original price p. Write and solve an equation to find the original price.

This article aims to find the original price of the ticket, given the discounted price and discount. The article uses the definitions of the original price, discount, and discounted price. To calculate original price of a discounted or sale item, you need to know the sale price and discount percentage. The calculations involve a simple formula that divides the sales price by $ 1 $ minus the percentage discount.

Use this formula to calculate the original or list price of an item.

\[ OP = \dfrac { price } { 1 – discount } \]

The term “discount” refers to a pricing system in which the price of a commodity (goods or service) is lower than its marked listed price. Simply put, a “discount” is a percentage of the listed price. A discount is a type of price reduction on products that are recorded in consumer transactions where buyers have proposed a certain percentage of discounts on various products to promote sales. This discount offered by the seller to the buyer is called a discount.

The discount is always calculated from the stated price, taking into account the selling price.

“Listed price” is the usual price of the goods without any discount.

“Sales Price” is the amount we actually pay to obtain the commodity at the time of purchase.

Expert Answer

Given information:

The discounted theme park ticket cost $ \$ 12.95 $ less than the original price $ p $. The price after the discount is $ \$ 44 $.

The original price is the sum of the discounted price and the discount.

\[ Original\: price = discounted\: price  +  discount \]

\[ p = 44 + 12.95 \]

\[ p = \$ 56.95 \]

The original price $ p = \$ 56.95 $.

Numerical Result

The original price $p =\$ 56.95$.

Example

A discounted theme park ticket costs $ \$ 14 $ less than the original price $ p $. Write and solve the equation to find the original price.

Solution:

\[ p = original\: price\: of \: the \: ticket \]

Let

\[ x = the \: discounted \: price  \]

The discounted price is $ \$ 14 $ less than the original price. Therefore:

\[ x = p \: – \: 14 \]

Add $ 14 $ on both sides.

\[ p = x + 14 \]

Let’s suppose that the discounted price is $ \$ 20 $.

\[ p = 34 \]

The original price is $ \$ 34 $.

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