To find the final cost of the skateboard including tax, follow these steps:
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Calculate the discount amount: \[ \text{Discount} = \text{Original Price} \times \text{Discount Rate} = 120 \times 0.15 = 18 \]
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Subtract the discount from the original price to find the sale price: \[ \text{Sale Price} = \text{Original Price} - \text{Discount} = 120 - 18 = 102 \]
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Calculate the sales tax on the sale price: \[ \text{Sales Tax} = \text{Sale Price} \times \text{Sales Tax Rate} = 102 \times 0.075 = 7.65 \]
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Add the sales tax to the sale price to find the final cost: \[ \text{Final Cost} = \text{Sale Price} + \text{Sales Tax} = 102 + 7.65 = 109.65 \]
Therefore, the final cost of the skateboard including tax is $109.65.