The expression 0.9(1.06 p) represents the total amount Zoe paid for a jacket originally priced p dollars. Which changes to the original price could have resulted in this expression? A discount of 0.9% and then 0.06% sales tax Sales tax of 106% and then a discount of 0.1% A discount of 10% and then 6% sales tax A discount of 90% and then 0.06% sales tax

Question

The expression  0.9(1.06 p) represents the total amount Zoe paid for a jacket originally priced  p dollars. Which changes to the original price could have resulted in this expression? A discount of  0.9% and then  0.06% sales tax Sales tax of  106% and then a discount of  0.1% A discount of  10% and then  6% sales tax A discount of  90% and then  0.06% sales tax

Bytelearn · Accepted Answer

Interpretation of Expression: The expression 0.9(1.06 p) can be interpreted as taking the original price p, multiplying it by 1.06 to account for an increase (such as a sales tax), and then multiplying the result by 0.9 to account for a decrease (such as a discount).Understanding Increase Factor: To understand the increase, we look at the factor 1.06. An increase by a factor of 1.06 corresponds to a 6% increase. This is because 1.06 is 100% of the original plus an additional 6%.Understanding Decrease Factor: To understand the decrease, we look at the factor 0.9. A factor of 0.9 corresponds to a 10% decrease. This is because 0.9 is 100% of the new amount after the increase minus a 10% discount.Comparison with Given Options: Now we compare the given options with our findings. The correct option should reflect a 6% increase followed by a 10% decrease.Analysis of Option A: Option A suggests a 0.9% discount followed by a 0.06% sales tax, which does not match our findings of a 10% discount and a 6% sales tax.Analysis of Option B: Option B suggests a 106% sales tax followed by a 0.1% discount, which is not consistent with our findings either.Analysis of Option C: Option C suggests a 10% discount followed by a 6% sales tax, which matches our findings exactly.Analysis of Option D: Option D suggests a 90% discount followed by a 0.06% sales tax, which is not consistent with our findings.

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