Understanding the Difference Between 50% and 33 1/3% Discounts

When evaluating discounts, it's important to understand how different percentages affect the final price of an item. This article delves into the specifics of a 50% discount versus a 33 1/3% discount, explaining the mathematical calculations behind each and summarizing the key differences.

Breaking Down the Discounts

To begin with, let's consider an item priced at $100. We will examine how each discount affects the original price.

50 Discount

A 50% discount is a straightforward way to calculate the amount saved:

If an item costs $100, a 50% discount would reduce the price by 50%.

Mathematically, this can be represented as:

$100 - (50% of $100)

The calculation is straightforward: 50% of $100 $50.

Therefore, the new price is:

$100 - $50 $50.

33 1/3 Discount

A discount of 33 1/3% is slightly more complex but can be easily understood as follows:

First, recognize that 33 1/3% is equivalent to 1/3 of the original price.

Thus, if an item costs $100, a 33 1/3% discount would reduce the price by approximately $33.33.

The calculation is:

$100 - (33 1/3% of $100)

The result is:

$100 - $33.33 $66.67.

Summary of the Differences

Discount Amount Saved Final Price 50% $50 $50 33 1/3% $33.33 $66.67

Conclusion

From this comparison, it is clear that a 50% discount offers a greater reduction in price compared to a 33 1/3% discount, resulting in a lower final price. This is evident when considering the difference between $50 and $66.67, which is $16.67 or 1/6 of the original price ($100).

Additional Insights

Considering a different example, where the full price of something is $300,:

With a 50% discount, you pay $150: 50% of $300 $150.

With a 33 1/3% discount, you pay $200: 33 1/3% of $300 $100, leaving $300 - $100 $200.

The difference between these is $50, which represents the difference in savings between the two discounts.

Turning these into fractions, 50% is 1/2 and 33 1/3% is 1/3, or 3/6 and 2/6 respectively. Therefore, the difference is 1/6 of the original price, further emphasizing the difference between the two discounts.