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Ryan goes to a store and buys an item that costs 
x dollars. He has a coupon for 
20% off, and then a 
8% tax is added to the discounted price. Write an expression in terms of 
x that represents the total amount that Ryan paid at the register.
Answer:

Ryan goes to a store and buys an item that costs x x dollars. He has a coupon for 20% 20 \% off, and then a 8% 8 \% tax is added to the discounted price. Write an expression in terms of x x that represents the total amount that Ryan paid at the register.\newlineAnswer:

Full solution

Q. Ryan goes to a store and buys an item that costs x x dollars. He has a coupon for 20% 20 \% off, and then a 8% 8 \% tax is added to the discounted price. Write an expression in terms of x x that represents the total amount that Ryan paid at the register.\newlineAnswer:
  1. Calculate Discount Amount: Calculate the discount amount.\newlineTo find the discount, we multiply the original price xx by the discount rate, which is 20%20\% or 0.200.20.\newlineDiscount = x×0.20x \times 0.20
  2. Calculate Discounted Price: Calculate the discounted price.\newlineSubtract the discount from the original price to find the sale price.\newlineSale price = x(x×0.20)x - (x \times 0.20)\newlineSimplify the expression.\newlineSale price = x0.20xx - 0.20x\newlineSale price = 0.80x0.80x
  3. Calculate Sales Tax: Calculate the sales tax on the discounted price.\newlineThe sales tax rate is 8%8\% or 0.080.08. We apply this rate to the sale price to find the tax amount.\newlineSales tax = 0.80x×0.080.80x \times 0.08
  4. Simplify Sales Tax Expression: Simplify the expression for the sales tax.\newlineSales tax = 0.80x×0.080.80x \times 0.08\newlineSales tax = 0.064x0.064x
  5. Calculate Total Amount Paid: Calculate the total amount paid.\newlineAdd the sales tax to the sale price to find the total amount paid.\newlineTotal amount paid =Sale price+Sales tax= \text{Sale price} + \text{Sales tax}\newlineTotal amount paid =0.80x+0.064x= 0.80x + 0.064x
  6. Simplify Total Amount Paid: Simplify the expression for the total amount paid.\newlineCombine like terms to get the final expression.\newlineTotal amount paid = 0.80x+0.064x0.80x + 0.064x\newlineTotal amount paid = 0.864x0.864x

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