Name Class Date. Solving Two-Step Equations

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1 Name Class Date 11-1 Solving Two-Step Equations Going Deeper Essential question: How do you solve equations that contain two operations? 1 CC7EE4a EXPLORE Solving Two-Step Equations video tutor Carrie and Freddy collect stamps Carrie notes that she has twelve less than five times the number of stamps Freddy has Carrie has 23 stamps Let f be the number of stamps that Freddy has A Write an equation that represents Carrie s collection B Method 1: Solve the equation by covering up the term with the variable 5f - 12 = = 23 Cover the term containing the variable Think: Some number minus 12 equals 23 = What number minus 12 equals 23? Now uncover the term 5f = Think: 5 times some number equals 35 5 times equals 35 f = C Method 2: Solve the equation by undoing the operations Step 1: Make a table First, list the operations in the equation according to the order in which they are applied to the variable Step 2: Apply the steps in the to solve column to solve the equation 5f - 12 = 23 Operations in the Equation 1 First f is by 5 2 Then, 12 is 1 First 12 to both sides of the equation 2 Then both sides by 5 Then, starting with the last operation in the equation write the opposite of the step Continue writing the opposite until every step is accounted for 5f - 12 = 23 5f = 35 f = Freddy has stamps Chapter Lesson 1

2 REFLECT 1a In what way are these two methods for solving equations similar? 1b To solve an equation, you isolate the variable by performing operations in the order from the order in which they are applied to the variable in the original equation 2 CC7EE4a explore Solving Two-Step Equations that Contain Fractions Use a table to help you solve each equation A 22 = n Operations in the Equation 1 First n is 1 First on both sides of the equation Solution 22 = n = n Then, 2 Then 15 = n 4 both sides by = n B 2x 3 = 12 Solution Operations in the Equation 1 First x is 2 Then, 1 First both sides by 2 Then both sides by 2x 3 = 12 2x 3 = 12 2x = 36 x = TRY THIS! Solve each equation 2a x = 40 2b x - 9 = 4 2c 2x 2 5 = 6 Chapter Lesson 1

3 3 CC7EE4a EXPLORE Solving Two-Step Equations that Contain Decimals Mai buys 3 new fish for her aquarium for a total of $969 Two of the fish are guppies, and the other is a white cloud The white cloud costs $319 What is the cost of each guppy? A Write an equation that can be used to find g, the cost in dollars of each guppy number of guppies times cost of one guppy plus cost of one white cloud equals total cost B Complete the table to decide how to undo the operations in the equation Operations in the Equation 1 First g is by 1 First from both sides of the equation 2 Then is to the product 2 Then both sides by C Use the steps from the column to solve the equation 2g = 969 2g = 969 2g = 2g = 65 g = The cost of each guppy is $ REFLECT 3a How could you check your answer to 3? TRY THIS! 3b Four friends equally split the cost of a pizza Garth pays for his share of the pizza plus a drink that costs $129 He pays a total of $478 Write and solve an equation to find c, the cost in dollars of the entire pizza Chapter Lesson 1

4 practice Solve each equation 1 6x + 8 = 26 2 n 3-4 = 5 3 3f 12 = c 1 4 = t 4-1 = m = a 4 = 36 8 s + 84 = Gabriella ran several laps around a 1 -mile track Then she ran 2 1 miles on a trail In all, she 4 2 ran 4 miles Write and solve an equation to find l, the number of laps Gabriella ran 10 Mario bought 3 cans of tennis balls He paid for part of the purchase using a gift card with $725 on it He paid for the rest with $472 of his own money Write and solve an equation to find c, the cost of each can of tennis balls Use the information about canoe and kayak rentals to solve each problem 11 Alisa and Chelsea paid a total of $31 to rent a canoe Write and solve an equation to find h, the number of hours they rented the canoe Canoe Rental $6 fee plus $10 per hour Kayak Rental $8 fee plus $8 per hour 12 Rick paid $24 to rent a kayak Adam paid $20 to rent a kayak How much longer did Rick rent a kayak than Adam did? Explain how you found your answer 13 Error Analysis Rochelle solve the equation 4x + 28 = 35 as shown at right Describe the error that Rochelle made What is the correct solution of the equation? 4x + 28 = 35 4x = x = 63 4x = x = 1575 Chapter Lesson 1

5 Name Class Date 11-1 Additional Practice Solve Check each answer 1 7x y a a k m 14 8 Solve 7 v u z f w e d u f Two years of local Internet service costs $685, including the installation fee of $85 What is the monthly fee? Chapter Practice and Problem Solving

6 Problem Solving Write the correct answer 1 Last week, Carlie had several rice cakes and 3 granola bars as snacks The snacks contained a total of 800 calories If each granola bar had 120 calories and each rice cake had 40 calories, how many rice cakes did she have? 2 Jo eats 2,200 calories per day She eats 450 calories at breakfast and twice as many at lunch If she eats three meals with no snacks, which meal will contain the most calories? 3 Erika is following a 2,200 calorieper-day diet She eats the recommended 9 servings of breads and cereals, averaging 120 calories per serving She also eats 5 servings of vegetables If the rest of her daily intake is 870 calories, what is the average number of calories in each serving of vegetables? 4 Brandon follows a 2,800 calorieper-day diet He has 11 servings of breads and cereals, which average 140 calories each Yesterday, he had a combined 9 servings of fruits and vegetables, averaging 60 calories each How many 180-calorie servings of meat and milk did he have to complete his diet? Choose the letter for the best answer The table shows calories burned by a person performing different activities 5 Kamisha swims for 025 hour How many calories does she burn? A 30 calories C 195 calories B 195 calories D 117 calories 6 Stu jogs at a rate of 5 mi/h How far must he jog to burn 4185 calories? F 9 mi H 375 mi G 465 mi J 45 mi 7 Terry rides her bike for 40 minutes and plays basketball for an hour How many calories does she burn? Calories Used in Activities Activity Calories (per min) Basketball 75 Cycling (10 mi/h) 55 Jogging 93 Swimming 78 8 How many hours would you have to ride your bike at 10 mi/h to burn 550 calories? A 67 calories C 670 calories F 167 hr H 10 hr B 560 calories D 1,300 calories G 15 hr J 075 hr Chapter Practice and Problem Solving