What is the single discount equivalent to the successive discounts of 20\%, 35\%, and 10\%?

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**Solution:**

1. Let the original price be 100%.

2. After the first discount of 20%, the price becomes:
   $$100\% - 20\% = 80\%$$

3. After the second discount of 35%, the price becomes:
   $$80\% 	imes (1 - 0.35) = 80\% 	imes 0.65 = 52\%$$

4. After the third discount of 10%, the price becomes:
   $$52\% 	imes (1 - 0.10) = 52\% 	imes 0.90 = 46.8\%$$

5. The final price is 46.8% of the original price, so the single equivalent discount is:
   $$100\% - 46.8\% = 53.2\%$$

**Answer:** The single discount equivalent to the successive discounts of 20\%, 35\%, and 10\% is **53.2\%**.

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