Math 95
Section 2.5
Applications involving Percents
Objectives:
Students will solve equations containing basic percent.
Students will solve applications involving simple interest and discount and markup.
Example:
338 is what percent of 520?
338  x  520  We are using multiplication since "of" means that here
338 520 x

520 520
0.65  x Keep in mind that we want a percent not a decimal
65%  x
Example:
What is 9.5% of 616?
x  .095  616  "What" is the unknown. Remember that % need to be put as decimals
x  58.52
Example:
594 is 45% of what number?
594  0.45 x
594 0.45 x

0.45 0.45
1320  x
Example:
In a recent survey of college-educated adults, 155 indicated that they regularly work
more than 50 hr a week. If this represents 31% of those surveyed, how many people
were in the survey?
So this problem is the same as saying “155 is 31% of what number?”
155  0.31x
155 0.31x

0.31 0.31
500  x
Example:
How much interest will Roxanne have to pay if she borrows $2000 for 2 years at a
simple interest rate of 4%?
In this problem, we will use the simple interest formula which is I = prt, where I is
interest, p is principal, r is rate, and t is time.
I  prt
I  2000  0.04  2 
I  160
Example:
If $9000 grows to $10,440 in 2 years, find the simple interest rate.
In this problem, we will use the formula A = P + Prt, where A is the amount with interest,
P is the principal, r is the rate, and t is time.
A  P  Pr t
10440  9000  9000r  2 
10440  9000  18000r
10440  9000  9000  9000  18000r
1440  18000r
1440 18000r

18000 18000
0.08  r
r  8%
Example:
The Avatar DVD is on sale for $18. If this represents an 18% discount rate, what was
the original price of the DVD?
In this problem, we will use the formula: Sale Price = Original Price – Discount. To find
the discount, you will take the original price times the discount rate.
Sale Price = Original Price - Discount
Sale Price = Original Price - Discount Rate x Original Price
18  x  0.18 x
18  0.88 x
18
0.88 x

0.88 0.88
21.95  x
Example:
In one area, the cable company marked up the monthly cost by 6%. The new cost is
$63.60 per month. What was the cost before the increase?
In this example, we will use the formula: New Cost = Old Cost + Markup. To find the
markup, you will take the old cost times the markup percent.
New Cost = Old Cost + Markup
New Cost = Old Cost + Old Cost x Markup Percent
63.60  x  0.06 x
63.60  1.06 x
63.60 1.06 x

1.06
1.06
60  x
Example:
A hotel room rented for 5 nights costs $706.25 including 13% in taxes. Find the original
price of the room (before tax) for the 5 nights. Then find the price per night.
In this problem, we will use almost the same formula as we did in the previous problem:
Final Cost = Original Cost + Tax. To find the tax, you will take the original cost x tax
rate.
Final Cost = Original Cost + Tax
Final Cost = Original Cost + Original Cost x Tax
706.25  x  0.13x
706.25  1.13x
706.25 1.13x

1.13
1.13
625  x But you have to remember that this is for 5 nights. We want 1 night.
625
 125
5
So it is $125 per night.