# Applications of Linear Equations

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Applications of Linear Equations
Math in Our World Section 6.3 Applications of Linear Equations

Learning Objectives Translate verbal expressions into mathematical symbols. Solve real-world problems using linear equations.

Common Phrases & Operations

Common Phrases & Operations

EXAMPLE 1 Translating Verbal Statements into Symbols
Translate each verbal statement into symbols. (a) 14 times a number (b) A number divided by 7 (c) 10 more than the product of 8 and a number (d) 3 less than 4 times a number (e) 6 times the sum of a number and 18

EXAMPLE 2 Solving a Basic Translation Problem
If 8 times a number plus 3 is 27, find the number.

Solving Word Problems Using Equations
Step 1 Read the Problem Carefully. Draw a diagram, jot down the key ideas Step 2 Devise a plan to solve the problem. Assign a variable to an unknown quantity, usually the quantity you’re being asked to find. Step 3 Write an equation. Keep an eye out for statements in the problem indicating two different ways to express the same quantity Step 4 Solve the equation. Step 5 Make sure that you answer the question! Step 6 Check to see if your solution makes sense.

EXAMPLE 3 A Problem Involving Contract Negotiations
Two basketball teams are interested in signing a free-agent player. An inside source informs the general manager of one team that the other has made an offer, and the player’s agent said “Double that and add an extra million per year, and you’re in our league.” According to a published report, the player is seeking a contract of \$18 million per year. What was the rival team’s offer?

EXAMPLE 4 An Application to Home Improvement
Pat and Ron are planning to build a deck off the back of their house, and they buy some plans from the Internet. The plans can be customized to the required deck height, which in this case will be 92 inches. They call for support posts of two different heights. The taller ones are 8 inches longer than the shorter ones, and the plans say that the sum of the lengths should be the height of the deck. How long should the support posts be cut?

EXAMPLE 5 An Application Involving Money
After a busy homecoming weekend, the tip jar at an off-campus bar is stuffed full of quarters and dollar bills. It turns out that there are 3 times as many quarters as dollar bills, and the jar contains \$140. How many quarters and how many dollar bills are there?

Classwork p : 5-53 eoo