Fabrizzio went shopping on Tuesday and decided to purchase a pair of pants that is $15 \%$ off the regular price. If he waits and buys the pants on Wednesday, he will receive an additional $5 \%$ off. What percent would Wednesday's sale price be of the original price for the pants? Round to the nearest whole percent. $\newline$ Choose $1$ answer: $\newline$ (A) $81 \%$ $\newline$ (B) $85 \%$ $\newline$ (C) $95 \%$ $\newline$ (D) $105 \%$

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Find what percent one number is of another: word problems

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Q. Fabrizzio went shopping on Tuesday and decided to purchase a pair of pants that is

15 \%

off the regular price. If he waits and buys the pants on Wednesday, he will receive an additional

5 \%

off. What percent would Wednesday's sale price be of the original price for the pants? Round to the nearest whole percent.

\newline

Choose

1

answer:

\newline

(A)

81 \%

\newline

(B)

85 \%

\newline

(C)

95 \%

\newline

(D)

105 \%

Calculate Percentage Tuesday Discount: Calculate the percentage of the original price that Fabrizzio pays on Tuesday after the $15\%$ discount. $\newline$ The formula for the sale price after a discount is: Sale Price $=$ Original Price $\times$ $(1 -$ Discount Percentage $)$ . $\newline$ For Tuesday, the discount percentage is $15\%$ , or $0.15$ as a decimal. $\newline$ So, the percentage of the original price he pays on Tuesday is $1 - 0.15 = 0.85$ or $85\%$ .
Calculate Effective Discount Wednesday: Calculate the effective discount on Wednesday. $\newline$ On Wednesday, there is an additional $5\%$ discount on the already reduced price. The additional discount is $5\%$ , or $0.05$ as a decimal. $\newline$ The effective discount on Wednesday is not simply $15\% + 5\% = 20\%$ , because the second discount is applied to the reduced price, not the original price.
Calculate Percentage Wednesday Discount: Calculate the percentage of the reduced price that Fabrizzio pays on Wednesday after the additional $5\%$ discount. $\newline$ The formula for the additional discount on Wednesday is: Wednesday Price $=$ Tuesday Price $\times (1 -$ Additional Discount Percentage $)$ . $\newline$ The percentage of the Tuesday price he pays on Wednesday is $1 - 0.05 = 0.95$ or $95\%$ .
Calculate Overall Percentage: Calculate the overall percentage of the original price that Fabrizzio pays after both discounts. $\newline$ To find the overall percentage, we multiply the percentages from Step $1$ and Step $3$ . $\newline$ Overall Percentage = $85\%$ (Tuesday's price as a percentage of the original price) $\times$ $95\%$ (Wednesday's price as a percentage of Tuesday's price). $\newline$ Convert these percentages to decimals for the calculation: $0.85 \times 0.95$ .
Perform Calculation Overall Percentage: Perform the calculation to find the overall percentage. $\newline$ Overall Percentage = $0.85 \times 0.95 = 0.8075$ . $\newline$ Convert this decimal back to a percentage by multiplying by $100$ : $0.8075 \times 100 = 80.75\%$ . $\newline$ Round to the nearest whole percent: $81\%$ .
Choose Correct Answer: Choose the correct answer from the options provided. $\newline$ The correct answer is (A) $81\%$ , as this is the rounded percentage of the original price that Wednesday's sale price would be.