Question

Business: Concession Markup A movie theater marks up the candy it sells by \(275 \%\). If a box of candy sells for 4.50 dollar at the theater, how much did the theater pay for the box?

Short answer

The theater paid 1.20 dollars for the box.

Step-by-step solution

- Understand the Markup

The markup percentage is 275%. This means the selling price is 275% more than the cost price.

- Set Up the Equation

Let the theater's cost price for the box of candy be denoted as \x\ dollars. The selling price adds the cost price plus 275% of the cost price. This can be represented by the following equation: \[ 4.50 = x + 2.75x \]

- Simplify the Equation

Combine the terms on the right-hand side: \[ 4.50 = 3.75x \]

- Solve for the Cost Price

Divide both sides of the equation by 3.75 to solve for \x\: \[ x = \frac{4.50}{3.75} = 1.20 \]

- Verify the Solution

To ensure the solution is correct, check if the selling price calculated from the cost price matches the given selling price: \[ 1.20 + 2.75 \cdot 1.20 = 4.50 \]

Key concepts

Percentage Markup

Percentage markup is the percentage amount by which a product's cost price is increased to determine its selling price. Imagine you bought a box of candy at a cost price, and the theater wants to make a profit. They increase the price by a certain percentage, known as the markup percentage. In our example, the markup is 275%.

Cost Price

The cost price is the initial amount paid for a product, before any markup is added. In our theater example, we wanted to find out how much the theater originally paid for the candy. This is the basis for calculating its selling price with markup.

Selling Price

The selling price is the price at which a product is sold to customers. It's calculated by taking the cost price and adding the markup amount. In our example, the box of candy sells for $4.50.

Algebraic Equations

Algebraic equations are useful tools for solving business problems. They help in expressing relationships between numbers and variables effectively. In our example with the box of candy, the equation represents the relationship between cost price and selling price with markup.