Math 1030
Percentage Problems
Name:___________________________
Recall the following important concept from chapter 3:
If A is P% more than B, then A is (100+P)% of B.
If A is P% less than B, then A is (100-P)% of B.
Example 1: If Nokia’s stock rose to $21.00 at the end of the week, up 7% over the
previous week’s close, then what was the price of Nokia’s stock at the previous week’s
close?
Solution: We know that the current stock price is $21.00, and it is 7% more than the stock
price of the previous week. In other words:
$21.00 is 7% more than B, so $21.00 is (100+7)% of B.
The variable B represents the old stock price, so we need to solve for B. We saw in class
that the word “is” means “=”, and the word “of” means “times” so we can rewrite the
statement $21.00 is (100+7)% of B as
$21.00 = 107% × B
$21.00 = 1.07 × B
$21.00
=B
1.07
$19.63 = B
So the price of Nokia’s stock at the previous week’s close was $19.63. If we wanted to
double check this answer, we could calculate the relative change between the new price
of $21.00 and the old price of $19.63. It should be 7%.
Example 2: The number of cancer related deaths in Greenville was 60 last year, down
20% from the previous year. How many cancer related deaths were there in Greenville
the previous year?
Solution: We know that
60 is 20% less than B, so 60 is (100-20)% of B
Where B represents the number of cancer related deaths in Greenvilee during the
previous year. We can write the statement that 60 is (100-20)% of B as
60 = 80% × B
60 = .8 × B
60
=B
.8
75 = B
So there were 75 cancer related deaths during the previous year. To check this answer,
you can again calculate the relative change. It should be -20%.
Exercises
1.) SomeCompany’s stock rose to $10.50 at the end of the week, up 5% over the
previous week’s close. What was the price of SomeCompany’s stock at the previous
week’s close?
2.) There were 54,902 licensed gun dealers in the U.S. in 2005, down 78% from 1994.
How many licensed gun dealers were in the U.S. in 1994?
3.) Sales of mobile video and navigation devices amounted to more than $450 million last
year, a 54% jump over the previous year. What were the sales in the previous year?
4.) Oracle’s stock dropped to $13.48 at the end of the week. Down 3% over the previous
week’s close. What was the price of Oracle’s stock at the previous weeks close?
5.) Suppose your home is worth $200,000. It is worth 12% more than it was last year, but
last year it was worth 5% less than the previous year.
a.) How much was your home worth last year?
b.) Use your answer from part (a) to find out how much your home was worth 2 years
ago.
6.) Suppose you get a job that pays $15 per hour.
a.)This job pays 15% more than your old job. What was your old hourly wage?
b.) Your old boss calls you and offers to pay you 15% more than he was paying you
before (15% more than the amount you calculated in part (a)). How much is he offering
to pay you hourly?