Page 492 - Basic College Mathematics with Early Integers

6.4 APPLICATIONS OF PERCENT Objectives

Solve Applications Involving
Percent.
Objective Solving Applications Involving Percent
Find Percent Increase and Percent
Percent is used in a variety of everyday
Decrease.
situations. The next examples show just Mount
a few ways that percent occurs in real- Katahdin,
Maine
life settings. (Each of these examples
shows two ways of solving these prob-
lems. If you studied Section 6.2 only, The
see Method 1. If you studied Section 6.3 Appalachian
only, see Method 2.) Trail
The first example has to do with
the Appalachian Trail, a hiking trail
Springer
conceived by a forester in 1921 and dia- Mountain,
grammed to the right. Georgia

Example 1 The circle graph in the margin shows the Appalachian Trail PRACTICE 1
mileage by state. If the total mileage of the trail is 2174, use the If the total mileage of the
circle graph to determine the number of miles in the state of New Appalachian Trail is 2174, use
York. Round to the nearest whole mile. the circle graph to determine
Solution: Method 1. First, we state the problem in words. the number of miles in the state
of Virginia.
In words: What number is 4% of 2174?
Appalachian Trail Mileage by State Percent
t
T T T T T
Georgia 4%
Translate: n = 4% # 2174 Maine 13% North Carolina 4%
Tennessee 14%
New Hampshire 7%
#
To solve for n, we find 4% 2174 . Vermont 7%
Virginia
25%
#
n = 0.04 2174 Write 4% as a decimal. Massachusetts 4%
Connecticut 2%
New York 4% West Virginia 0.2%
n = 86.96 Multiply. New Jersey 3% Maryland 2%
Pennsylvania 11%
n L 87 Round to the nearest whole.
Total miles: 2174
Source: purebound.com
Rounded to the nearest whole mile, we have that approximately 87 miles of the Note: In order to represent each state along the Trail, the total of these percents is 100.2%.
Appalachian Trail are in New York state.
Method 2. State the problem in words; then translate.
In words: What number is 4% of 2174?
t
T T T
amount percent base
Translate: amount : a 4 ; percent
=
base : 2174 100
Next, we solve for a.
#
#
a 100 = 2174 4 Set cross products equal.
#
a 100 = 8696 Multiply.
#
a 100 8696
= Divide both sides by 100.
100 100
a = 86.96 Simplify.
a L 87 Round to the nearest whole.
Rounded to the nearest whole mile, we have that approximately 87 miles of the
Appalachian Trail are in New York state. Answer
1. 543.5 mi
Work Practice 1
469