1. Applications of Algebra

2. Chapter Sections 3.1 – Changing Application Problems into Equations
3.2 – Solving Application Problems
3.3 – Geometric Problems
3.4 – Motion, Money and Mixture Problems
Chapter 1 Outline

3. Changing Application Problems into Equations

4. Word or Phrase Statement Algebra
Operations
Statement
Algebra
Added to
More than
Increased by
The sum of
Addition
A number added to 3
2 more than a number
A number increased by 7
The sum of a 1 and a number
3 + x
x + 2
x + 7
1 + x
Subtracted from
Less than
Decreased by
Difference between
The difference in
The difference of
Subtraction
A number subtracted from 3
5 less than a number
A number decreased by 8
The difference between 4 and a number
The difference in a number and 6
The difference of x squared and y squared
3 - x
x – 5
x – 8
4 - x
x – 6
x2- y2
Multiplied by
The product of
Twice a number
Three times a number
Of (when used with a percent or fraction)
Multiplication
8 multiplied by a number
The product of 9 and a number
25% of a number 8x 9x 2x 3x
0.25x
Divided by
The quotient of
The ratio of
Division
13 divided by a number
The quotient of a number and 11
The ratio of a number and 17

5. Expressions with Percents
Percent means “per one hundred.”
Statement
Expression
A 7.5% sales tax on c dollars
The cost, c, increased by 7.5%
The cost, c, reduced by 25%
0.075c
c c
c – 0.25c

6. Translating into Equations
The word is often means is equal to and is represented by an equal sign.
Statement
Equation
Six times a number is 42.
Five more than twice a number is 4.
7 decreased by a number is 4 more than twice the number.
The sum of a number and the number increased by 4 is 60.
6x = 42
2x + 5 = 4
7- x = 2x + 4
x + (x + 4) = 60