Li wants to buy a skateboarding helmet and pads. She sees a set she likes at a sporting goods store. The set costs $54.99. It is on sale for 30% off. Li has a coupon that will take an additional 10% off the sale price. She lives in a state that charges 5.75% sales tax. How much will Li have to earn to pay for the skateboarding set?
First find the price reduction by multiplying the price by the discount: $54.99 * 30% = $<<54.99*30*.01=16.50>>16.50.
Then subtract the discount from the original price to find the sale price: $54.99 - $16.50 = $<<54.99-16.50=38.49>>38.49
Then multiply the sale price by the additional discount percentage: $38.49 * 10% = $<<38.49*10*.01=3.85>>3.85
Subtract the additional discount from the sale price to find the final price before tax: $38.49 - $3.85 = $<<38.49-3.85=34.64>>34.64
Multiply the price before tax by the sales tax rate to find how much tax Li pays: $34.64 * 5.75% = $<<34.64*5.75*.01=1.99>>1.99
Add the price before tax and the sales tax to find the final price Li pays: $34.64 + $1.99 = $<<34.64+1.99=36.63>>36.63. Answer: \boxed{36.63}.