MHB Introductory Algebra Percentage Word Problem

AI Thread Summary
The discussion revolves around a percentage word problem involving a dress marked down first by 20% and then by an additional 15%, resulting in a final price of $51. The initial calculations incorrectly added the discount percentages, leading to a misunderstanding of the final sale price as 65% of the original price. The correct approach shows that after both discounts, the final price is actually 68% of the original price. The original price is calculated to be $75, not $78.46, confirming that the book's answers are accurate. Understanding the sequential nature of percentage reductions is crucial for solving such problems correctly.
Larry2527
Messages
1
Reaction score
0
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?

- - - Updated - - -

Er, it posted all garbled for some reason. I have no idea why. Any ideas?
 
Mathematics news on Phys.org
Larry2527 said:
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.
 
Larry2527 said:
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?
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...

Similar threads

Replies
1
Views
2K
Replies
3
Views
1K
Replies
1
Views
1K
Replies
8
Views
5K
Replies
2
Views
4K
Replies
2
Views
7K
Back
Top