MHB Introductory Algebra Percentage Word Problem

[Larry2527]

The problem as given in the book:

The price of a dress is marked down 20% on May 1. On May 25th the reduced price is marked down an additional 15% to \$51. (a) What percent of the original price is the final sale price? (b) "What is the original price?

All I could think was trying to work the problem this way:

(a) 20% + 15% = 35% (total discount percentage)
100% - 35% = 65% (percent of the original price for a sale price of \$51)

(b) 65%x = \$51
x = 51/.65
x = \$78.46 (original price)

The answer given in the back of the book is given as (a) 68% and (b) \$75. Assuming the book's answer is correct, what am I missing?

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Er, it posted all garbled for some reason. I have no idea why. Any ideas?

 

[skeeter]

The problem as given in the book:

The price of a dress is marked down 20% on May 1. On May 25th the reduced price is marked down an additional 15% to \$51. (a) What percent of the original price is the final sale price? (b) "What is the original price?

All I could think was trying to work the problem this way:

(a) 20% + 15% = 35% (total discount percentage)
100% - 35% = 65% (percent of the original price for a sale price of \$51)

(b) 65%x = \$51
x = 51/.65
x = \$78.46 (original price)

The answer given in the back of the book is given as (a) 68% and (b) \$75. Assuming the book's answer is correct, what am I missing?

Let $P$ be the original price.

first reduction to $0.80P$

second reduction to $0.85(0.80P) = 0.68P = 51 \implies P = 75$

the final price is 68% of $P = 75$

fyi, dollar signs activate the latex math type on this site. if you want to use one without doing so, put a backward slash \ prior to the dollar sign.

 

[HallsofIvy]

The problem as given in the book:

The price of a dress is marked down 20% on May 1. On May 25th the reduced price is marked down an additional 15% to \$51. (a) What percent of the original price is the final sale price? (b) "What is the original price?

All I could think was trying to work the problem this way:

(a) 20% + 15% = 35% (total discount percentage)

There is your mistake! A percentage is always a percent of something (the "base" number). You cannot add these percentages because they are of different bases. The first is 20% of the original price. The second is 15% of that new price.

Let P be the original price. Then after the first mark down, the price is P'= P- 0.20P= 0.80P. After the second markdown, the price is P'- 0.15P'= 0.85P'= 0.85(0.80P)= 0.68P, or 68% of the original price, not 65%.

0.68P= 51 so P= 51/0.68

100% - 35% = 65% (percent of the original price for a sale price of \$51)

(b) 65%x = \$51
x = 51/.65
x = \$78.46 (original price)

The answer given in the back of the book is given as (a) 68% and (b) \$75. Assuming the book's answer is correct, what am I missing?

- - - Updated - - -

Er, it posted all garbled for some reason. I have no idea why. Any ideas?