Page 621 - Basic College Mathematics with Early Integers

598 C HAPTE R 8 I INTRODUCTION TO ALGEBRA

4. INTERPRET the results. First, check the proposed solution in the stated prob-
lem.Twice “-9” is -18 and -18 + 3 is -15. This is equal to the number minus
6, or “-9” - 6, or -15. Then state your conclusion:The unknown number is -9.
Work Practice 3

Concept Check Suppose you have solved an equation involving perimeter
to find the length of a rectangular table. Explain why you would want to recheck
your math if you obtain the result of -5.

PRACTICE 4 Example 4 Determining Distances
The distance by road from The distance by road from Chicago, Illinois, to Los Angeles, California, is 1091
Cincinnati, Ohio, to Denver, miles more than the distance from Chicago to Boston, Massachusetts. If the total
Colorado, is 71 miles less than of these two distances is 3017 miles, find the distance from Chicago to Boston.
the distance from Denver to (Source:World Almanac)
San Francisco, California. If the
total of these two distances is Solution:
2399 miles, find the distance
from Denver to San Francisco. 1. UNDERSTAND the problem.We read and reread the problem.
Let’s propose and check a solution to help us better understand the prob-
Chicago
Cincinnati lem. Suppose the distance from Chicago to Boston is 600 miles. Since the dis-
tance from Chicago to Los Angeles is 1091 more miles, then this distance is
San
Francisco Boston 600 + 1091 = 1691 miles. With these numbers, the total of the distances is
Los 600 + 1691 = 2291 miles. This is less than the given total of 3017 miles, so we
Angeles
are incorrect. But not only do we have a better understanding of this exercise,
Denver
we also know that the distance from Boston to Chicago is greater than 600
miles since this proposed solution led to a total too small. Now let’s choose a
variable to represent an unknown.Then we’ll use this variable to represent any
other unknown quantities. Let
x = distance from Chicago to Boston

Then
x + 1091 = distance from Chicago to Los Angeles
since that distance is 1091 more miles.
2. TRANSLATE the problem into an equation.
In words:
Chicago to Chicago to Los
+ = total miles
Boston distance Angeles distance
T T T
v
Translate: x + x + 1091 = 3017
3. SOLVE the equation:
x + x + 1091 = 3017
2x + 1091 = 3017 Combine like terms.
2x + 1091 - 1091 = 3017 - 1091 Subtract 1091 from both sides.
2x = 1926 Simplify.
2x 1926
= Divide both sides by 2.
2 2
Answer x = 963 Simplify. Copyright 2012 Pearson Education, Inc.
4. 1235 miles
4. INTERPRET the results.First check the proposed solution in the stated problem.
Concept Check Answer Since x represents the distance from Chicago to Boston, this is 963 miles. The
Length cannot be negative. distance from Chicago to Los Angeles is x + 1091 = 963 + 1091 = 2054 miles .