To find out how much Li will have to earn to pay for the skateboarding set, we need to calculate the final cost of the set, including the discount and sales tax.
First, let's calculate the discount on the set. The set is on sale for 30% off, so we can find the discount amount using the following formula:
Discount = 30% * $54.99
Discount = 0.30 * $54.99
Discount = $16.50
Now we can find the sale price of the set after the discount:
Sale Price = Original Price - Discount
Sale Price = $54.99 - $16.50
Sale Price = $38.49
Next, we can calculate the additional discount Li gets with her coupon. The coupon will take an additional 10% off the sale price, so we can find the additional discount using the following formula:
Additional Discount = 10% * $38.49
Additional Discount = 0.10 * $38.49
Additional Discount = $3.85
Now we can find the final price of the set after applying the additional discount:
Final Price = Sale Price - Additional Discount
Final Price = $38.49 - $3.85
Final Price = $34.64
Finally, we need to calculate the sales tax on the final price. The state charges 5.75% sales tax, so we can find the sales tax amount using the following formula:
Sales Tax = 5.75% * $34.64
Sales Tax = 0.0575 * $34.64
Sales Tax = $1.99
Adding the sales tax to the final price gives us the total amount Li will have to earn to pay for the skateboarding set:
Total Amount = Final Price + Sales Tax
Total Amount = $34.64 + $1.99
Total Amount = $36.63
Therefore, Li will have to earn $36.63 to pay for the skateboarding set.