Transcript Changing Application Problems into Equations

MTH 10905
Algebra
CHANGING APPLICATION
PROBLEMS INTO EQUATIONS
CHAPTER 3 SECTION 1
Translate Phrases into Mathematical Expressions
What to look for….word and phrases
What they mean…..operation
Added to
More than
Increased by
The sum of
Addition
7 added to a number
7+x
Subtract from
Less than
Decreased by
The difference between
Subtraction
7 less than a number
Multiplied by
The product of
Twice a number, three times a number, etc
Of, when used with a percent or fraction
Multiplication
The product of 4 and a number 4x
Twice a number 2x
20% of a number 0.20x
Divided by
The quotient of
Division
A number divided by 4
Will be
Was
Yields
Equal sign
The number of cents in d, dimes is
120
10d = 120
x–7
x/4
Translate Phrases into Mathematical Expressions
 A number decreased by 5
x–5
(6 – 5) = 1
Not the same as….be careful when writing your equations.
5 decreased by a number
5–x
(5 – 6) = -1
 Commas are also a key to writing an expression
 Three times a number, decreased by 4
3x – 4
not the same as
three times a number decreased by 4
3(x – 4)
Translate Phrases into Mathematical Expressions
 Sometimes we may have more than one expression.
 EXP:
four more than, twice a number
2x + 4
 EXP:
five less than, three times a number
3x – 5
 EXP :
three times, the sum of a number and 8
3(x + 8)
 EXP:
five inches less than twice the height, h
2h – 5
 The first thing you need to do to write an expression or equation is to
determine what quantity to let the variable represent
Express a relationship between two related quantities
 EXP:
John is 3 year older than 4 times Sue’s age
Let x = Sue’s age
4x + 3 = John’s age
 EXP:
A 30 foot board is cut into two lengths. Select a variable
to represent one of the lengths. Then write an expression
to represent the other length.
Let l = first length
30 – l = second length
Write expressions involving multiplication
 EXP:
Write an expression for “the cost for mailing x letters at 39
cents each”
0.39x
 EXP:
Tim rented a tractor for 1 day. He paid a delivery fee of
$80 and a usage fee of $200 per hour. Write an
expression for the total cost when he uses the tractor for h
hours.
80 + 200h
 EXP:
Fred’s age is one less than twice Alice’s age. Write an
expression for the difference in Fred and Alice’s age.
let x = Alice
2x – 1 = Fred
2x – 1 – x
Translate Applications into Equations
 EXP:
Express the statement “the profit, p, decreased by 15%” as
an algebraic expression.
let p = profit
0.15 p = 15% decrease
p – 0.15p
 EXP:
Write the following as an equation.
“The cost of p pens at $2.20 per pen is $25
let p = number of pens
2.20 p = cost of p pens
2.20p = 25
Translate Applications into Equations
 EXP:
Write the following as an equation.
“one number is 6 less than three times the other”
Their sum is 22
let x = first number
3x – 6 = second number
x + (3x – 6) = 22
 EXP:
Translate the following into an equation
“Ursula’s GPA increased by 8.2”
“Her new GPA is 3.4”
let x = old
0.082x = new
x + 0.082x = 3.4
Remember
 You can use any letter to represent the variable. x is the most common.
 More than one pair of expressions can be used to represent two
numbers. “two numbers differ by 5”
x = first number
x – 5 = second number
 Consecutive integers differ by 1
EXP: 2 and 3
Represented by x and x + 1
 Consecutive even integers differ by 2
EXP: 6 and 8
EXP: 7 and 9
and Consecutive odd integers differ by 2
represented by x and x + 2
x is always the smaller integer and x + 2 is always the larger integer
HOMEWORK 3.1
 Page 191 - 193
#57, 61, 63, 65, 69, 96, 101, 104