Understanding discounts and markups is essential when solving percent problems related to price changes. A discount refers to the amount by which the price of an item decreases, while a markup is the amount by which the price increases. Both concepts can be addressed using the fundamental percent equation, which calculates the partial amount by multiplying the percent (expressed as a decimal) by the whole amount.

For example, consider a used gaming system originally priced at $385 that is sold at an 85% discount. To find the discount amount, convert 85% to its decimal form, 0.85, and multiply it by the original price:

$$ \text{Discount} = 0.85 \times 385 = 327.25 $$

This means the price decreases by $327.25. To find the new sale price, subtract the discount from the original price:

$$ \text{New Price} = 385 - 327.25 = 57.75 $$

Thus, the discounted price is $57.75.

Similarly, when dealing with a markup, such as an engagement ring purchased wholesale for $1,800 with a 70% markup, the markup amount is found by multiplying 70% (0.70) by the original price:

$$ \text{Markup} = 0.70 \times 1800 = 1260 $$

The new price after the markup is the sum of the original price and the markup amount:

$$ \text{New Price} = 1800 + 1260 = 3060 $$

Therefore, the ring’s retail price is $3,060.

In summary, solving discount and markup problems involves identifying the percent change, converting it to a decimal, and multiplying by the original price to find the partial amount. The new price is then calculated by subtracting the discount or adding the markup to the original price. Mastering this approach allows for efficient and accurate solutions to a wide range of real-world percent problems involving price adjustments.

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