Download Chapter 3 Applications of Algebra Chapter 3-1

Chapter 3
Applications
of Algebra
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-1
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
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-2
2
Changing Application
Problems into
Equations
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-3
3
Word or Phrase Operations
Added to
More than
Increased by
The sum of
Subtracted from
Less than
Decreased by
Difference between
The difference in
The difference of
Multiplied by
The product of
Twice a number
Three times a number
Of (when used with a
percent or fraction)
Addition
Subtraction
Multiplication
Divided by
The quotient of
The ratio of
Statement
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
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
8 multiplied by a number
The product of 9 and a number
Twice a number
Three times a number
25% of a number
8x
9x
2x
3x
0.25x
13 divided by a number
Division
Algebra
The quotient of a number and 11
The ratio of a number and 17
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
13
x x
11 x
17
Chapter 3-4
4
Expressions with Percents
Percent means “per one hundred.”
Statement
A 7.5% sales tax on c dollars
The cost, c, increased by 7.5%
The cost, c, reduced by 25%
Expression
0.075c
c + 0.075c
c – 0.25c
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 3-5
5
Translating into Equations
The word is often means is equal to and is
represented by an equal sign.
Statement
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.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Equation
6x = 42
2x + 5 = 4
7- x = 2x + 4
x + (x + 4) = 60
Chapter 3-6
6