Name Class Date Practice -2 Writing Two-Step Equations 8-2 Writing Two-Step Equations. Last night, 4 friends went out to dinner at a restaurant. They split the bill evenly. Each friend paid $2.75. If B represents the total bill in dollars, what equation could you use to find the value of B? A. B + 4 = 2.75 C. B. 4B = 2.75 B 4 = 2.75 D. B 4 = 2.75 2. A garden contains 25 flowers, each of which is either red or orange. There are 60 orange flowers. If R represents the number of red flowers in the garden, what equation could you use to find the value of R? A. R 25 = 60 C. 60R = 25 B. R + 60 = 25 D. R 60 = 25 3. A farmer ships oranges in crates that weigh 6. lb each when empty. Each orange weighs 0.38 lb. The total weight of a crate filled with oranges is 63. lb. Write a word equation you could use to find the number of oranges packed in each crate. A. total weight = weight of crate + (weight of one orange) (number of oranges) B. total weight = weight of crate + weight of one orange + number of oranges C. total weight = (weight of crate) (weight of one orange) + number of oranges D. total weight = weight of crate (weight of one orange) (number of oranges) E. total weight = (weight of crate) (weight of one orange) (number of oranges) 4. At a graduation dinner, an equal number of guests were seated at each of 3 large tables, and 7 late-arriving guests were seated at a smaller table. There were 37 guests in all. If n represents the number of people seated at each of the large tables, what equation could you use to find the value of n? A. 3n 7 = 37 C. 7n + 3 = 37 B. 3n + 7 = 37 D. 7n 3 = 37 5. Which answer shows the equation 7x 8 = 7 in words? A. Eighteen less than seven times a number is 7. B. Seven less than eighteen times a number is 7. C. Seven more than eighteen times a number is 7. D. Eighteen more than seven times a number is 7.
6. Write an equation to represent the following description. Nineteen less than seven times a number is. 7. a) Writing You want to buy a pet iguana that costs $48. You already have $2 and you plan to save $9 per week. If w represents the number of weeks until you have enough money to buy the iguana, what equation could you use to find the value of w? A. 9 2w = 48 D. 2 9w = 48 B. 2w 9 = 48 E. 9w 2 = 48 C. 9w + 2 = 48 F. 2w + 9 = 48 b) Explain how you could set up an equation to find the amount of money you should save each week if you want to buy the iguana in six weeks. 8. a) Reasoning In a certain country, the life expectancy of a woman born in 995 was 80.2 years. In 2005, the life expectancy was 0.8 years greater. If L represents the life expectancy of a woman born in 2005, what equation could you use to find the value of L? A. L 0.8 = 80.2 C. L + 80.2 = 0.8 B. L + 0.8 = 80.2 D. L 0 = 0.8 b) Could two different equations be used to find the value of L? Explain your reasoning. 9. Error Analysis The difference of three times a number and fourteen is six. Tristan incorrectly claimed the equation 4 3x = 6 represents the description. a) What is the correct equation? A. 3 4x = 6 D. 3x 4 = 6 B. 4x + 3 = 6 E. 3x + 4 = 6 C. 4x 3 = 6 F. 6 3x = 4 b) What error might Tristan have made? A. He used subtraction instead of addition. B. He subtracted 3x from the wrong number. C. He used the wrong number as the coefficient of x. D. He subtracted the terms in the wrong order. 0. Banner One of the banners in a parade is one-third as tall as it is long. It is 5 feet tall. If L represents the length of the banner in feet, what equation could you use to find the value of L? A. 3 = 5L C. 5 = L 3 B. 5 = 3 L D. L = 5 3 2
7 5. Estimation A rectangle has length 3 inches and area 6 square inches. 8 6 Round these measurements to the nearest integer. Let w represent the width of the rectangle in inches. Which of these equations correctly relates the rectangle s length and width to its area? A. 4w = 6 C. w + 4 = 7 4 B. 4w = 7 D. = 7 w 2. a) Open-Ended Which of these descriptions could the equation 6x 7 = 26 represent? Check all that apply. A. The difference between sixteen times a number and seventeen B. The difference between seventeen times a number and sixteen C. When sixteen times a number is decreased by seventeen, the result D. When seventeen times a number is decreased by sixteen, the result E. The sum of sixteen times a number and seventeen F. The sum of seventeen times a number and sixteen G. When seventeen times a number is increased by sixteen, the result H. When sixteen times a number is increased by seventeen, the result b) Describe at least two real-world situations that could produce this equation. 3. You buy 2.25 pounds of plums and.95 pound of oranges. Plums and oranges sell for the same price per pound. The total cost, after using a 55 -off coupon, is $3.23. If c represents the cost of the fruit in dollars per pound, what equation could you use to find the value of c? A. 2.25c 0.55 = 3.23 D. 3.65c + 0.55 = 3.23 B..95c + 55 = 3.23 E. 4.2c 0.55 = 3.23 C. 4.2c + 0.55 = 3.23 F. 4.2c 55 = 3.23 4. a) Challenge Which of these descriptions does the equation 5x 3 = 2 represent? Check all that apply. A. Thirteen more than five times a number is 2. B. If you subtract thirteen times a number from five, you get 2. C. If you add thirteen to five times a number, you get 2. D. If you subtract thirteen from five times a number, you get 2. E. Five less than thirteen times a number is 2. F. Five more than thirteen times a number is 2. G. Thirteen less than five times a number is 2. H. If you subtract five from thirteen times a number, you get 2. b) Of the numbers, 2, 3, 4, and 5, which are solutions to the equation? 3
5. Challenge If you decrease three times a number by six, you get 6. a) Which equation represents the description? A. 6x + 3 = 6 B. 6x 3 = 6 C. 3(x 6) = 6 b) Is 4 a solution to the equation? D. 3x + 6 = 6 E. 3x 6 = 6 c) Show how to apply the same operation to each side of the equation to get an equivalent equation that has only one operation. 4
ANSWER KEY : Writing Two-Step Equations. C 2. B 3. A 4. B 5. A 6. 7x 9 = 7. a) C 8. a) A 9. a) D b) D 0. B. B 2. a) A, C 3. E 4. a) D, G b) 3 5. a) E b) Yes c) Answers will vary 5 Answer Key G