134 Chapter 2 Linear Equations and Inequalities aLength of one piece b a length of other piece b a total length x 4x 6 4x 4 x 1.5 of the board 6 4 x 1.5 311.5 ft2 4.5 ft. b Using a Linear Equation in an Application Example 7 The hit movie Harry Potter and the Deathly Hallows: Part 2 set a record for grossing the most money during its opening weekend. This amount surpassed the previous record set by the movie The Dark Knight by $10.8 million. The revenue from these two movies was $327.6 million. How much revenue did each movie bring in during its opening weekend? Solution: In this example, we have two unknowns.The variable x can represent either quantity. Step 1: Read the However, the revenue from Harry Potter is problem. given in terms of the revenue for The Dark Knight. Let x represent the revenue for The Dark Knight. Step 2: Label the variables. Then represents the revenue for Harry Potter. 327.6 Step 4: Write an equation. Step 5: Solve the equation. x 1x 10.82 2x 10.8 327.6 2x 316.8 x 158.4 • Revenue from The Dark Knight: x 158.4 • Revenue from Harry Potter: x 10.8 158.4 10.8 169.2 The revenue from Harry Potter and the Deathly Hallows:Part 2 was $169.2 million for its opening weekend.The revenue for The Dark Knight was $158.4 million. a Revenue from The Dark Knight b arevenue from Harry Potter b a total revenue b x 10.8 Step 3: Write a verbal model. 3x 6 Step 4: Write an equation. Step 5: Solve the equation. The smaller piece is ft. Step 6: Interpret the results. The longer piece is 3x or Skill Practice 6. A plumber cuts a 96-in. piece of pipe into two pieces. One piece is five times longer than the other piece. How long is each piece? 13 x x 13 x 6 Answer 6. One piece is 80 in. and the other is 16 in. Step 3: Write a verbal model. TIP: The variable can represent either unknown. In Example 6, if we let x represent the length of the longer piece of board, then would represent the length of the smaller piece. The equation would become . Try solving this equation and interpreting the result.
miller_beginning_intermediate_algebra_4e_ch1_3
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