1. Thinking Mathematically
Algebra: Equations and Inequalities
6.3 Applications of Linear Equations

2. Algebraic Translations of English Phrases
See Table 6.2
Examples
8 is decreased by 5 times a number
The quotient of 15 and a number
The sum of twice a number and 20
30 subtracted from 7 times a number

3. Strategy for Solving Word Problems
Before you start: Read the problem carefully at least twice. Attempt to state the problem in your own words and state what the problem is looking for.
Step 1: Let x (or any variable) represent one of the quantities in the problem.
Step 2: If necessary, write expressions of any other unknown quantities in the problem in terms of x.
Step 3: Write an equation in x that describes the verbal conditions of the problem.

4. Strategy for Solving Word Problems
Step 4: Solve the equation and answer the problem’s question.
Step 5: Check the solution in the original wording of the problem, not in the equation obtained from the words.

5. Examples: Word Problems
Exercise Set 6.3 #9, 29
One number exceeds another by 26. The sum of the numbers is 64. What are the numbers.
A new car worth $24,000 is depreciating n value by $3,000 per year. After how many years will the car’s value be $9,000?

6. Examples: Word Problems
Exercise Set 6.3 #33, 39
The bus fare in a city is $ People who use the bus have the option of purchasing a monthly coupon book for $ With the coupon book, the fare is reduced to $ Determine the number of times in a month the bus must be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book.
After a 20% reduction, you purchase a television for $336. What was the television’s price before the reduction?

7. Thinking Mathematically
Algebra: Equations and Inequalities
6.3 Applications of Linear Equations