25. a furniture store is advertising a 20% discount on the price of sofas. scott chooses a sofa with a…

25. a furniture store is advertising a 20% discount on the price of sofas. scott chooses a sofa with a discounted price of $460.00. he must also pay an 8% sales tax. how much money will scott save on the discounted sofa, including tax, compared to the originally priced sofa, including tax? $

25. a furniture store is advertising a 20% discount on the price of sofas. scott chooses a sofa with a discounted price of $460.00. he must also pay an 8% sales tax. how much money will scott save on the discounted sofa, including tax, compared to the originally priced sofa, including tax? $

Answer

Answer:

$115$

Explanation:

Step1: Find the original price of the sofa

Let the original price be $x$. After a $20%$ discount, the price is $(1 - 20%)x=0.8x$. Given $0.8x = 460$, then $x=\frac{460}{0.8}=575$.

Step2: Calculate the price with tax for the discounted sofa

The price of the discounted sofa is $460$. With an $8%$ sales - tax, the total cost is $460\times(1 + 8%)=460\times1.08 = 496.8$.

Step3: Calculate the price with tax for the original - priced sofa

The original price of the sofa is $575$. With an $8%$ sales - tax, the total cost is $575\times(1 + 8%)=575\times1.08=621$.

Step4: Calculate the amount saved

The amount saved is $621-496.8 = 115$.