MTH 10905Algebra

CHANGING APPLICATION PROBLEMS INTO EQUATIONS

CHAPTER 3 SECTION 1

Translate Phrases into Mathematical Expressions

Added toMore thanIncreased byThe sum of

Addition 7 added to a number7 + x

Subtract fromLess thanDecreased byThe difference between

Subtraction 7 less than a number x – 7

Multiplied byThe product ofTwice a number, three times a number, etcOf, when used with a percent or fraction

Multiplication The product of 4 and a number 4xTwice a number 2x20% of a number 0.20x

Divided byThe quotient of

Division A number divided by 4 x/4

Will beWasYields

Equal sign The number of cents in d, dimes is 120 10d = 120

What to look for….word and phrases What they mean…..operation

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 ageLet x = Sue’s age4x + 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 length30 – 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 = profit0.15 p = 15% decreasep – 0.15p

EXP: Write the following as an equation. “The cost of p pens at $2.20 per pen is $25let p = number of pens2.20 p = cost of p pens2.20p = 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 22let x = first number3x – 6 = second numberx + (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 = newx + 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 numberx – 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

and Consecutive odd integers differ by 2 EXP: 7 and 9represented by x and x + 2

x is always the smaller integer and x + 2 is always the larger integer

HOMEWORK 3.1

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