Final answer:
Max's claim of saving 15% altogether is not correct without considering the individual costs of each item. You must calculate the actual savings on each item separately and then relate it to the total original cost to find the correct overall savings percentage.
Step-by-step explanation:
Max's statement that he saved 15% altogether on two items, one with a 10% discount and the other with a 20% discount, is not necessarily correct. To determine if Max saved 15% overall, we need to consider the individual costs of each item.
Understanding the Calculation of Total Sales Discount
When combining different percentage discounts on separate items, you cannot simply take the average of the two percentages unless the items cost the same amount. Instead, you must calculate the savings for each item individually and then find the combined savings as a percentage of the total original cost.
For example:
- If the first item costs $100 with a 10% discount, Max saves $10 on this item.
- If the second item also costs $100 with a 20% discount, Max saves $20 on this one.
The total savings would be $10 + $20 = $30, and since the total original cost is $200 ($100 + $100), the overall percentage saved is $30/$200 = 0.15, which is a 15% savings.
However, if the items had different original costs, then the overall percentage saved would likely differ. The correct way to calculate the combined discount percentage is by finding the total savings in dollars from both items and then dividing by the total original cost of both items.
Step-by-Step Example
Let's consider two separate items, where the first item costs $200, and the second item costs $150.
- First item's savings: $200 x 0.10 = $20
- Second item's savings: $150 x 0.20 = $30
- Total savings: $20 + $30 = $50
- Total original cost: $200 + $150 = $350
- Overall percentage saved: $50 / $350 ≈ 0.1429, or approximately 14.29%
This example demonstrates that the actual overall percentage saved is different from what Max presumed unless each item had the same cost. Thus, to accurately determine the combined savings percentage, Max should use the above method.