Questions: A movie theater marks up the candy it sells by 350%. If a box of candy sells for 8.10 at the theater, how much did the theater pay for the box?

Solution Steps

To find out how much the theater paid for the box of candy, we need to reverse the markup calculation. Given that the markup is 350%, we can use the formula for markup:

\[ \text{Selling Price} = \text{Cost Price} + (\text{Markup Percentage} \times \text{Cost Price}) \]

Rearranging this formula to solve for the Cost Price:

\[ \text{Cost Price} = \frac{\text{Selling Price}}{1 + \text{Markup Percentage}} \]

Given:

• Selling Price = $8.10
• Markup Percentage = 350% = 3.5 (as a decimal)

We can now plug these values into the formula to find the Cost Price.

We are given:

• Selling Price \( S = \$8.10 \)
• Markup Percentage \( M = 350\% = 3.5 \) (as a decimal)

The formula to find the Cost Price \( C \) from the Selling Price and Markup Percentage is: \[ C = \frac{S}{1 + M} \]

Substitute \( S = 8.10 \) and \( M = 3.5 \) into the formula: \[ C = \frac{8.10}{1 + 3.5} \]

Calculate the denominator: \[ 1 + 3.5 = 4.5 \]

Now, divide the Selling Price by this value: \[ C = \frac{8.10}{4.5} \]

Perform the division: \[ C = 1.8 \]

Final Answer