Thinking Mathematically

Algebra: Equations and Inequalities

6.3 Applications of Linear Equations

Algebraic Translations of English Phrases

See Table 6.2

Examples8 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

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.

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.

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?

Examples: Word Problems

Exercise Set 6.3 #33, 39• The bus fare in a city is $1.25. People who use the bus

have the option of purchasing a monthly coupon book for $15.00. With the coupon book, the fare is reduced to $0.75. 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?

Thinking Mathematically

Algebra: Equations and Inequalities

6.3 Applications of Linear Equations