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The expression 
0.75(1.08 p) represents the total amount Amelia paid for a jacket originally priced 
p dollars. Which changes to the original price could have resulted in this expression?
A discount of 
25% and then 
0.08% sales tax
A discount of 
25% and then 
108% sales tax
A discount of 
25% and then 
8% sales tax
A discount of 
0.25% and then 
108% sales tax

The expression 0.75(1.08p) 0.75(1.08 p) represents the total amount Amelia paid for a jacket originally priced p p dollars. Which changes to the original price could have resulted in this expression?\newlineA discount of 25% 25 \% and then 0.08% 0.08 \% sales tax\newlineA discount of 25% 25 \% and then 108% 108 \% sales tax\newlineA discount of 25% 25 \% and then 8% 8 \% sales tax\newlineA discount of 0.25% 0.25 \% and then 108% 108 \% sales tax

Full solution

Q. The expression 0.75(1.08p) 0.75(1.08 p) represents the total amount Amelia paid for a jacket originally priced p p dollars. Which changes to the original price could have resulted in this expression?\newlineA discount of 25% 25 \% and then 0.08% 0.08 \% sales tax\newlineA discount of 25% 25 \% and then 108% 108 \% sales tax\newlineA discount of 25% 25 \% and then 8% 8 \% sales tax\newlineA discount of 0.25% 0.25 \% and then 108% 108 \% sales tax
  1. Interpret Expression: Understand the expression 0.75(1.08p)0.75(1.08p). The expression can be interpreted as taking 75%75\% of some amount (which is the same as a 25%25\% discount), and then increasing that result by 8%8\% (which could represent a sales tax).
  2. Break Down Parts: Break down the expression into two parts.\newlineThe first part is 0.750.75, which represents a 75%75\% portion of the original price, pp. This implies that the original price has been reduced by 25%25\% because 100%75%=25%100\% - 75\% = 25\%.
  3. Analyze Increase: Analyze the second part of the expression, which is 1.081.08. This represents an increase of the amount after the discount by 8%8\%. This is typically how sales tax is applied, as a percentage increase on the price after discounts.
  4. Compare to Options: Compare the expression to the given options.\newlineThe expression 0.75(1.08p)0.75(1.08p) matches the scenario where there is a discount of 25%25\% followed by an 8%8\% sales tax. This corresponds to option C: "A discount of 25%25\% and then 8%8\% sales tax."