Page 98 - Basic College Mathematics with Early Integers

1.8 AN INTRODUCTION TO PROBLEM SOLVING Objectives

Solve Problems by Adding,
Subtracting, Multiplying, or
Objective Solving Problems Involving Addition, Dividing Whole Numbers.
Subtraction, Multiplication, or Division
Solve Problems That Require
In this section, we decide which operation to perform in order to solve a problem. More Than One Operation.
Don’t forget the key words and phrases that help indicate which operation to use.
Some of these are listed below and were introduced earlier in the chapter. Also
included are several words and phrases that translate to the symbol “=”.

Addition Subtraction Multiplication Division Equality
#
(+) (-) () (÷) (=)
sum difference product quotient equals
plus minus times divide is equal to
added to subtract multiply shared equally is/was
more than less than multiply by among yields
increased by decreased by of divided by
total less double/triple divided into

The following problem-solving steps may be helpful to you:

Problem-Solving Steps PRACTICE 1

1. UNDERSTAND the problem. Some ways of doing this are to read and The Bank of America Building
reread the problem, construct a drawing, and look for key words to identify is the second-tallest building in
an operation. San Francisco, California, at
779 feet.The tallest building
2. TRANSLATE the problem. That is, write the problem in short form using in San Francisco is the
words, and then translate to numbers and symbols.
Transamerica Pyramid, which is
3. SOLVE the problem. It is helpful to estimate the solution by rounding.Then 74 feet taller than the Bank of
carry out the indicated operation from step 2. America Building. How tall is
4. INTERPRET the results. Check the proposed solution in the stated problem the Transamerica Pyramid?
and state your conclusions.Write your results with the correct units attached. (Source:The World Almanac)

Example 1 Calculating the Length of a River
74 feet
The Hudson River in New York State is 306 miles long. The Snake River in the
northwestern United States is 732 miles longer than the Hudson River. How long
779 feet
is the Snake River? (Source: U.S. Department of the Interior)
Solution:
?
1. UNDERSTAND. Read and reread the problem, and then draw a picture.
Notice that we are told that Snake River is 732 miles longer than the Hudson
River.The phrase “longer than” means that we add.

306 miles

Hudson River
732 miles
Bank of America Transamerica
Pyramid
Snake River
Answer
Continued on next page
1. 853 ft
75