1-1. Variables and Expressions

Transcription

1 exploration Catherine s dance team is planning a spring trip to the coast. Catherine is saving money in a bank account to pay for the trip. Her parents started her account with $100. She sells Christmas plants and adds $2.50 to her account for each plant she sells. How much will be in her account if she sells 50 plants? Initial amount Price number of plants n Evaluate the expression n by substituting 50 for n (50) There will be $ in Catherine s account if she sells 50 plants. Evaluate the expression n for each value of n. 1. n (10) 2. n ( ) 3. n ( ) Think and Discuss 4. Explain why n is called the variable in the expression n. 5. Describe how to evaluate an expression. This page is available as a transparency. 7 Holt Middle School Math

2 Exploration Recording Sheet Catherine s dance team is planning a spring trip to the coast. Catherine is saving money in a bank account to pay for the trip. Her parents started her account with $100. She sells Christmas plants and adds $2.50 to her account for each plant she sells. How much will be in her account if she sells 50 plants? Initial amount Price number of plants n Evaluate the expression n by substituting 50 for n (50) There will be $ in Catherine s account if she sells 50 plants. Evaluate the expression n for each value of n. 1. n (10) 2. n ( ) 3. n ( ) Think and Discuss 4. Explain why n is called the variable in the expression n. 5. Describe how to evaluate an expression. 8 Holt Middle School Math

3 Practice A Evaluate each expression y for y x for x 3 3. a 11 for a r 8 for r b for b y for y f 32 for f t for t k for k s 21.4 for s x y for x 7 and y ab for a 1.5 and b j h for h 9 and j a b for a 6 and b c 6d for c 5 and d (x y) for x 18 and y 14 The cost of greeting cards at Discount Cards Plus is $0.60. How much does it cost for each number of greeting cards? cards cards cards cards 21. Mrs. Williams is driving on the interstate at a rate of 58 mi/h. a. Write an expression for the distance she will drive in x hours at this rate. b. How far will she drive in 4.5 hours at this rate? 9 Holt Middle School Math

4 Practice B Evaluate each expression for the given value of the variable. 1. 6x 2for x a for a y for y b for b n for n k for k (b 15) for b n(18 5) for n 4 Evaluate each expression for the given value of the variables. 9. 2x y for x 7 and y j k for j 4 and k a 6b for a 6 and b s 5t for s 15 and t (n m) for m 4 and n w(14 y) for w 8 and y 5 A lemonade mix calls for 1 4 cup of mix for one quart of lemonade. How much mix is needed to make each amount of lemonade? quarts quarts quarts quarts 19. For each ride, Bill s Taxi Company charges $2 plus $0.35 for each minute. a. Write an expression for the cost of a taxi ride of x minutes. b. How much will it cost for a 12-min taxi ride? 10 Holt Middle School Math

5 Practice C Evaluate each expression for the given value of the variable a 8for a (7 b) for b (8 n) 2 for n (x 9) for x (k 6) 20 for k ( j 3.7) for j (d 6) for d y(4 6) 5 for y c(16 9) for c p 4p 13 for p 9 Evaluate each expression for a 3, b 2.5, c 7, and d b 8d 12. 5(b c) 13. ab c (a d) b 15. 9abc 16. 7b 12c 5a If g is Jamaal s gross pay, then g 0.2g can be used to find his take home pay after 20% is taken out for taxes. Find Jamaal s take home pay for each gross pay amount. 17. $ $ $ $ All sweaters at Knit Inc. are on sale for 15% off the regular price. a. Write an expression for the sweater price after the discount. b. What is the sale price of a sweater that is regularly $34? 11 Holt Middle School Math

6 Reteach An algebraic expression uses at least one letter, or variable, which represents a value that can change. A number that multiplies a variable is its coefficient. A constant is a specific number, whose value does not change. To evaluate an algebraic expression, substitute a given number for a variable, and find the value of the resulting numerical expression. Algebraic Expression 4x 7 Coefficient Constant Variable Follow the order of operations: 1. Parentheses 2. Multiply or Divide 3. Add or Subtract Evaluate 5(m 1) 8n for m 10 and n 2. 5(m 1) 8n 5(10 1) 8(2) Substitute 10 for m and 2 for n. 5(11) 8(2) Parentheses, simplify inside Multiply, from left to right. 71 Add. Complete to evaluate each expression z for z (q 8) for q x for x ( 8) 25 2 ( ) 9 5 ( ) (x 6) 4 for x (x 1) for x (2z) for z 4 2( 6) ( 1) 22 5 (2 ) 2( ) ( ) 22 5 ( ) Holt Middle School Math

7 Challenge Etaulave: Evaluate Backwards Expression Value for Variable Substitution Value of Expression 2x 5 1 2(1) 5 7 2x 5 2 2(2) 5 9 2x 5 3 2(3) 5 11 In the table above you use the values of the variable to evaluate the given expression. What if you are given the values of the expression and the values of the variable? How can you work backward to determine the expression? Expression Value for Variable Substitution Value of Expression Complete the following statements. 1. As the values of the variable increase by 1, the values of the expression increase. 2. Because the values of the expression depend on the values of the variables, your answer to Question 1 tells you the of the variable. 3. Using the coefficient and the variable x, you know that is part of the expression. 4. After each value of the variable is multiplied by, you still need to to get the value of the expression. Write the expression given the values of x and their corresponding values of the expression. 5. The values of the expression are 12, 14, 16, 18, 20 when x 10, 11, 12, 13, and The values of the expression are 50, 45, 40, 35, 30 when x 2, 3, 4, 5, and Holt Middle School Math

8 Problem Solving Write the correct answer. 1. If l is the length of a room and w is the width, then lw can be used to find the area of the room. Find the area of a room with l 15 ft and w 10 ft. 2. If l is the length of a room and w is the width, 2l 2w can be used to find the perimeter of the room. Find the perimeter of a room with l 16 ft and w 12 ft. 3. Jaime earns 20% commission on her sales. If s is her total sales, then 0.2s can be used to find the amount she earns in commission. Find her commission if her sales are $ If p is the regular hourly rate of pay, then 1.5p can be used to find the overtime rate of pay. Find the overtime rate of pay if the regular hourly rate of pay is $6.00 per hour. Choose the letter for the best answer. 5. A plumber charges a fee of $75 per service call plus $15 per hour. If h is the number of hours the plumber works, then 75 15h can be used to find the total charges. Find the total charges if the plumber works 2.5 hours. A $37.50 B $ C $225 D $ If c is the number of cricket chirps in a minute, then the expression c 4 20 can be used to estimate the temperature in degrees Farenheit. If there are 92 cricket chirps in a minute, find the temperature. A 43 degrees B 33 degrees C 102 degrees D 75 degrees 6. Tickets to the movies cost $4 for students and $6 for adults. If s is the number of students and a is the number of adults, 4s 6a can be used to find the cost of the tickets. Find the cost of the tickets for 3 students and 2 adults. F $15 G $17 H $24 J $26 8. Flowers are sold in flats of 6 plants each. If f is the number of flats, then 6f can be used to find the number of flowers. Find the number of flowers in 18 flats. F 3 flowers G 108 flowers H 24 flowers J 12 flowers 14 Holt Middle School Math

9 Puzzles, Twisters & Teasers Running the Roads of New Mexico What is the state bird of New Mexico? Evaluate the expressions below for the given variables. Put the letter above each expression in the decoder to find the answer. 1. R 2. T 3. D x 6 g 5 y 12 12x 4g 6 3y U 5. N 6. A z 60 m 8 x 9 2z 5m 35 3x O 8. H 9. E a 12 t 25 y 11 9a 16t 4 6y Holt Middle School Math