Page 447 - Basic College Mathematics with Early Integers

424 C HAPTE R 5 I RATIO, PROPORTION, AND MEASUREMENT

Chapter 5 Group Activity

Sections 5.1–5.7 Consumer Price Index 3. In 2000, the cost of a loaf of bread was about $1.89.
Do you remember when the regular price of a candy bar What would an equivalent loaf of bread have cost in
was 5¢, 10¢, or 25¢? It is certainly difficult to find a candy 1950?
bar for that price these days. The reason is inflation: the 4. Suppose a couple purchased a house for $12,000 in
tendency for the price of a given product to increase 1940.At what price could they have been expected to
over time. Businesses and government agencies use the sell the house in 1990?
Consumer Price Index (CPI) to track inflation. The CPI 5. An original Ford Model T cost about $850 in 1915.
measures the change in prices over time of basic con- What is the equivalent cost of a Model T in 2008
sumer goods and services. dollars?
The CPI is very useful for comparing the prices of
fixed items in various years. For instance, suppose an Consumer Price Index
insurance company customer submits a claim for the
theft of a fishing boat purchased in 1975. Because the Year CPI
customer’s policy includes replacement cost coverage, 1915 10.1
the insurance company must calculate how much it
would cost to replace the boat at the time of the theft. 1920 20.0
(Let’s assume the theft took place in February 2010.)
1925 17.5
The customer has a receipt for the boat showing that it
cost $598 in 1975. The insurance company can use the 1930 16.7
following proportion to calculate the replacement cost:
1935 13.7
price in earlier year CPI value in earlier year 1940 14.0
=
price in later year CPI value in later year
1945 18.0
The CPI value is 53.8 for 1975. In February 2010, the 1950 24.1
CPI value was 216.9.The insurance company would then
1955 26.8
use the following proportion for this situation. (We will
let n represent the unknown price in February 2010.) 1960 29.6
price in 1975 CPI value in 1975 1965 31.5
=
price in 2010 CPI value in Feb. 2010
1970 38.8
598 53.8
= 1975 53.8
n 216.9
# 1980 82.4
53.8 n = 5981216.92
#
53.8 n = 129,706.2 1985 107.6
#
53.8 n 129,706.2 1990 130.7
=
53.8 53.8 1995 152.4
n L 2411 2000 172.2
The replacement cost of the fishing boat at February 2005 195.3
2010 prices is $2411.
2006 201.6
Critical Thinking 2007 207.3
Copyright 2012 Pearson Education, Inc.
1. What trends do you see in the CPI values in the table? 2008 215.3
Do you think these trends make sense? Explain.
2009 214.5
(Source: Bureau of Labor Statistics, U.S.
2. A piece of jewelry cost $800 in 1985. What is its 2005 Department of Labor)
replacement value?