Certainly! Let's break down the problem of finding a single discount equivalent to two successive discounts of 25% and 8%.
1. Starting Point: Let's assume the original price of an item is [tex]$100. This choice simplifies the calculations, and percentages can be easily converted to dollar amounts.
2. First Discount (25%):
- A 25% discount on the original price of $[/tex]100 can be calculated by multiplying:
[tex]\[
\text{First discount amount} = 100 \times 0.25 = 25
\][/tex]
- Subtract this discount from the original price:
[tex]\[
\text{Price after first discount} = 100 - 25 = 75
\][/tex]
3. Second Discount (8%):
- Next, we apply an 8% discount on the new price of [tex]$75:
\[
\text{Second discount amount} = 75 \times 0.08 = 6
\]
- Subtract this second discount from the price after the first discount:
\[
\text{Price after second discount} = 75 - 6 = 69
\]
4. Effective Discount:
- To find the overall discount from the original price of $[/tex]100 to the final price of $69:
[tex]\[
\text{Total discount amount} = 100 - 69 = 31
\][/tex]
- Convert this discount amount to a percentage of the original price:
[tex]\[
\text{Effective discount percentage} = \left(\frac{31}{100}\right) \times 100 = 31\%
\][/tex]
So, the single discount equivalent to successive discounts of 25% and 8% is 31%.
