Introductory Algebra Percentage Word Problem

In summary: 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 = \$51x = 51/.65x = \
  • #1
1
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
  • #2
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.
 
  • #3
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?
 

1. What is the formula for solving percentage word problems in introductory algebra?

The formula for solving percentage word problems in introductory algebra is: Part = Percent x Whole. This formula is also known as the proportion method.

2. How do I convert a percentage to a decimal?

To convert a percentage to a decimal, divide the percentage by 100. For example, 35% would be converted to a decimal by dividing 35 by 100, which equals 0.35. This decimal can then be used in the proportion method to solve percentage word problems.

3. What is the difference between a percentage and a percent?

There is no difference between a percentage and a percent. They are two ways of representing the same concept - a portion or part of a whole expressed in terms of a hundred.

4. How do I find the percentage increase or decrease in a word problem?

To find the percentage increase or decrease in a word problem, use the formula: Percent Change = (New Value - Original Value) / Original Value x 100. If the result is positive, it is a percentage increase. If the result is negative, it is a percentage decrease.

5. Can I use the proportion method to solve any type of percentage word problem?

Yes, the proportion method can be used to solve any type of percentage word problem as long as the problem involves finding a part, whole, or percent. It is a versatile and reliable method for solving percentage problems in introductory algebra.

Suggested for: Introductory Algebra Percentage Word Problem

Replies
1
Views
1K
Replies
4
Views
1K
Replies
44
Views
3K
Replies
22
Views
243
Replies
1
Views
599
Replies
2
Views
617
Replies
2
Views
1K
Replies
4
Views
145
Replies
4
Views
768
Back
Top