What percentage discount from the base price results in an optimal order quantity of 101 sheets?

Understand the Problem

The question is asking for the calculation of the percentage discount from a base price for drywall sheets when purchasing an optimal order quantity of 101 sheets. The context given details the cleanup job requiring a specific amount of drywall and the associated costs depending on the quantity purchased.

Answer

The percentage discount from the base price is approximately $2.13\%$.

Steps to Solve

Identify Base Price and Discounted Price

The base price for drywall sheets is $9.40 per sheet for quantities of 1-20 sheets. For 101 or more sheets, the price per sheet is $9.20.

Calculate the Discount Amount

To find the discount amount, subtract the discounted price from the base price:

$$ \text{Discount} = \text{Base Price} - \text{Discounted Price} $$

Substituting the values:

$$ \text{Discount} = 9.40 - 9.20 = 0.20 $$

Calculate the Percentage Discount

The percentage discount is found by dividing the discount amount by the base price and then multiplying by 100:

$$ \text{Percentage Discount} = \left( \frac{\text{Discount}}{\text{Base Price}} \right) \times 100 $$

Substituting the values:

$$ \text{Percentage Discount} = \left( \frac{0.20}{9.40} \right) \times 100 $$

Calculating this gives:

$$ \text{Percentage Discount} \approx 2.13% $$

The percentage discount from the base price for an optimal order quantity of 101 sheets is approximately $2.13%$.

More Information

A discount symbolizes the savings when purchasing in larger quantities. Understanding the steps to calculate percentage discounts is essential for budgeting and making cost-saving decisions.

Tips

Miscalculating the difference between the base price and discounted price.
Forgetting to multiply by 100 when calculating the percentage.
Confusing the order of operations, leading to incorrect calculations.

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