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Section 2.4
An Introduction to Applications of Linear Equations
Solving an Applied Problem
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Read the problem carefully until you understand what is given and what is to be found.
Assign a variable to represent the unknown value, using diagrams or tables as needed.
Write down what the variable represents. If necessary, express any other unknown
values in terms of the variable.
Write an equation using the variable expression(s).
Solve the equation.
State the answer. Does it seem reasonable?
Check the answer in the words of the original problem.
Example 1
If 5 is added to the product of 9 and a number, the result is 19 less than the number. Find the
number.
(Assign the variable . Write an equation and solve.)
Example 2
In the 2006 Winter Olympics in Torino, Italy, the United States won 6 more medals than Norway.
The two countries won a total of 44 medals. How many medals did each country win?
(Assign the variable . Write an equation and solve.)
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Example 3
The owner of Terry’s Coffeehouse found that the number of orders for croissants was 1/6 the
number of orders for muffins. If the total number for the two breakfast rolls was 56, how many
orders were placed for croissants?
(Assign the variable . Write an equation and solve.)
Example 4
At a meeting of the local computer user group, each member brought two nonmembers. If a
total of 27 people attended, how many were members and how many were nonmembers?
(Assign the variable . Write an equation and solve.)
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Example 5
A piece of pipe is 50 in. long. It is cut into three pieces. The longest piece is 10 in. more than the
middle-sized piece, and the shortest piece measures 5 in. less than the middle-sized piece. Find
the lengths of the three pieces.
(Assign the variable . Write an equation and solve.)
Definition: Two integers that differ by 1 are called consecutive integers.
Examples:
5 and 6
102 and 103
-3 and -2
If x represents an integer, then _________ represents the next larger consecutive integer.
Consecutive even integers and consecutive odd integers differ by 2.
Examples:
4 and 6 (consecutive even integers)
7 and 9 (consecutive odd integers)
If x represents an even integer, then _________ represents the next larger even consecutive integer.
If x represents an odd integer, then _________ represents the next larger odd consecutive integer.
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Example 6
Two back-to-back page numbers in this book have a sum of 569. What are the page numbers?
(Assign the variable . Write an equation and solve.)
Example 7
Find two consecutive even integers such that six times the lesser added to the greater gives a
sum of 86.
(Assign the variable . Write an equation and solve.)