226 algebra De mystif ieD
- 54 increased by 21.3% is 54 + (0.213)(54) = 54 + 11.502 = 65.502
- 128 decreased by 8.16% is 128 – (0.0816)(128) = 128 – 10.4448 = 117.5552
- 15 increased by 0.03% is 15 + (0.0003)(15) = 15 + 0.0045 = 15.0045
- 24 decreased by 108.4% is 24 – (1.084)(24) = 24 – 26.016 = –2.016
Many word problems involving percents fit the above model—that is, a quantity
being increased or decreased by a percent of the original quantity.EXAMPLE
A $100 jacket will be reduced by 15% for a sale. What will the sale price be?
Let x = sale price. Because the price is decreased, we use the model
“Original Price – 15% ×× Original Price = Sale Price” to compute the sale price.
Then, 100 – (0.15)(100) = x
100 – 15 = x
85 = x
The sale price is $85.We usually see a price after it has been reduced. We can solve an equation to
find the original price. Again, the equation isSale Price = Original Price – Percent of the Original PriceEXAMPLE
The sale price for a computer is $1200, which represents a 20% markdown.
What is the original price?
We let x represent the original price, so the sale price is x – 0.20x = 0.80x.
The sale price is also 1200. These two facts give us the equation 0.80x =
1200.080 1200
1200
080
1500.
.x
x
x=
=
= The original price is $1500.EXAMPLE
A $100 jacket will be reduced by 15% for a sale. What will the sale price be?EXAMPLE
The sale price for a computer is $1200, which represents a 20% markdown.