1. MTH 10905 Algebra CHANGING APPLICATION PROBLEMS INTO EQUATIONS CHAPTER 3 SECTION 1

2. Translate Phrases into Mathematical Expressions Added to More than Increased by The sum of Addition7 added to a number 7 + x Subtract from Less than Decreased by The difference between Subtraction7 less than a number x – 7 Multiplied by The product of Twice a number, three times a number, etc Of, when used with a percent or fraction MultiplicationThe product of 4 and a number 4x Twice a number 2x 20% of a number 0.20x Divided by The quotient of DivisionA number divided by 4 x/4 Will be Was Yields Equal signThe number of cents in d, dimes is 120 10d = 120 What to look for….word and phrases What they mean…..operation

3. 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 number5 – 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)

4. Translate Phrases into Mathematical Expressions Sometimes we may have more than one expression. EXP: four more than, twice a number2x + 4 EXP:five less than, three times a number3x – 5 EXP :three times, the sum of a number and 83(x + 8) EXP: five inches less than twice the height, h2h – 5 The first thing you need to do to write an expression or equation is to determine what quantity to let the variable represent

5. 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

6. 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

7. 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

8. 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

9. 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 1EXP: 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 2EXP: 7 and 9 represented by x and x + 2 x is always the smaller integer and x + 2 is always the larger integer

10. HOMEWORK 3.1 Page 191 - 193 #57, 61, 63, 65, 69, 96, 101, 104