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