What single discount is equivalent to two successive discounts of 15% and 7%?

x= 100 [1-(.85)(.93)] = 100 (1-.79) =100 (.21) =21%

yes, good job

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To find the equivalent single discount, we need to calculate the final price after applying two successive discounts and then find the single discount that would give us the same final price.

Let's start with a original price of 100.

First, we apply a discount of 15%. To do this, we multiply the original price by (1 - 0.15) or 0.85. This gives us the price after the first discount: 100 * 0.85 = 85.

Now, we apply a second discount of 7%. We multiply the price after the first discount by (1 - 0.07) or 0.93. This gives us the final price after applying both discounts: 85 * 0.93 = 79.05.

So, the final price after applying two successive discounts of 15% and 7% is 79.05.

To find the equivalent single discount, we need to calculate the percentage decrease from the original price to the final price of 79.05.

The formula for the percentage decrease is (original price - final price) / original price * 100.

Substituting the values, we get (100 - 79.05) / 100 * 100 ≈ 20.95.

Therefore, a single discount of approximately 20.95% is equivalent to the two successive discounts of 15% and 7%.