Name: Date: Lesson 17 Word Problems Day 1

Transcription

1 Name: Date: Lesson 17 Word Problems Day 1 Warm Up Foldable Algebraic Expression vs Algebraic Equation Model Problems (a) An example of an algebraic expression is (b) An example of an algebraic expression is (c) An example of an algebraic expression is (d) Mr. Stanton asked his students to write an algebraic expression on a piece of paper. He chose four students to go to the board and write their expression. Robert wrote: Meredith wrote: Steven wrote: Cynthia wrote: Which student wrote an algebraic expression? Robert Meredith Steven Cynthia 1

2 Practice Problems Directions: Identify each as an algebraic expression(aex) or an algebraic equation(aeq) x = 10-6x + 2x 11 3x + 7y 4v + 2 < 10 5) 9 x ) 6x 7) 8x + 9y + z 8) 1 = 2x + 7 9) 2x 4 10) 15w 3 = 2w Translate a Quantitative Verbal Phrase into an Algebraic Expression *highlight/underline key words English Math seven more than n difference of n and 7 product of seven and n quotient of n and seven five less than n 2

3 Practice Problems Directions: Match the verbal expression with the mathematical expression. 1. Three times the sum of a number and 5 (a) 5x Six less than twice a number (b) 3. Five less than half of a number (c) 6 4x + 2 x 2x Four times the difference of a number squared and six. (d) x Eight less than four times a number (e) ¾x 5 6. Twice the sum of a number and seven. (f) 2x 6 7. Ten less than five times a number cubed (g) 2x Three times the difference of a number squared and 15 (h) ½x 5 9. Sixteen less than the quotient of twice a number and five 10. A number squared increased by twice the sum of another number cubed and six 11. The sum of a four times a number and six divided by the number squared (i) 4x 8 (j) 2 x 12 3 (k) 3(x+5) 12. Two-thirds of a number decreased by twelve (l) 3(x 2 15) 13. The square of a number decreased by six (m) 2(x+7) 14. Twice the sum of a number and five (n) 2(x+5) 15. Five less than three-fourths of a number (o) X 2 + 2(x 3 + 6) 16. Four less than the difference of a number squared and six (p) 4(x 2 6) 17. The sum of twice a number and 7 (q) (x 2 6) 4 3

4 Regents Questions Which verbal expression represents? two times n minus six two times six minus n two times the quantity n less than six two times the quantity six less than n Which verbal expression can be represented by? 5 less than 2 times x 2 multiplied by x less than 5 twice the difference of x and 5 the product of 2 and x, decreased by 5 Which algebraic expression represents 15 less than x divided by 9? 5) Which verbal expression is represented by? one-half n decreased by 3 one-half n subtracted from 3 the difference of one-half n and 3 one-half the difference of n and 3 Which expression represents 5 less than twice x? 6) Which verbal expression is represented by? twice the sum of a number and four the sum of two times a number and four two times the difference of a number and four twice the product of a number and four Writing Expressions from a Situation Model Problems (a) *Francesca makes y dollars each day. Write an expression for the number of dollars Francesca will make in w weeks. (b) *Carlos currently owns 5 toy cars. He plans on buying x cars each week for w weeks. Write an expression to represent the total number of cars he will have. (c) *Write an expression to represent the number of minutes in d days. (d) *Jose bought a pair of pants and two shirts for h dollars. Each shirt cost s dollars. Write an expression to represent the number of dollars it cost Jose for the pants. 4

5 Practice Problems Regents Questions *Marie currently has a collection of 58 stamps. If she buys s stamps each week for w weeks, which expression represents the total number of stamps she will have? *If Angelina s weekly allowance is d dollars, which expression represents her allowance, in dollars, for x weeks? *Which expression represents the number of hours in w weeks and d days? *Timmy bought a skateboard and two helmets for a total of d dollars. If each helmet cost h dollars, the cost of the skateboard could be represented by 5) *Mr. Turner bought x boxes of pencils. Each box holds 25 pencils. He left 3 boxes of pencils at home and took the rest to school. Which expression represents the total number of pencils he took to school? 6) *A bus holds 30 people, and a van holds 10 people. Which of the following expressions shows the number of people that could fill b buses and v vans? 7) *Write an expression for the number of tokens need for v video games if each game takes 4 tokens. 8) * Write an expression for the total it would cost for 8 chairs at c dollars each and a $400 table. 5

6 9) *Jared earns 0.25 vacation days for every week that he works in a calendar year. He also gets 10 paid company holidays per year. Write an expression to represent the amount of time he gets off work in a year after working for w weeks. 10) *Richard went to the airport and paid $273 for his ticket, $25 in fees and $13 each day to park. Write an expression to model Richard s payment to park for d days. 1 *Write an expression to determine how many minutes you have left if you had a total of 250 minutes and you talked an hour a week for w weeks. 1 *José bought a CD storage box for D dollars and a dozen CDs for c dollars each. The store deducted these costs from his paycheck of P dollars. (a) Write an expression for the cost of the CDs. (b) Write an expression to determine how much was left from José's paycheck after buying the CDs and storage box? 1 *It costs $.50 per word, plus $10.50 to make a customized license plate frame for a car. Write an expression for the total cost of making p license plate frames with w words on it. 1 *Jet-skis Unlimited rents Jet-skis at a local lake for $20 per each 15 minutes, plus a $9.50 insurance fee for the rental. Write an expression for the cost to rent a jet-ski from Jet-skis Unlimited for t 15 minute intervals. Summary 6

7 Name: Date: Word Problems Day 1 7