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Warm Up

Use Problem Solving Strategies and Models. Warm Up. Lesson Presentation. Lesson Quiz. Warm-Up. Solve the equation. 1. 780 = 12.5 r. ANSWER. 62.4. 2. 9 x + 25 = 178. 17. ANSWER. ANSWER. 11. Warm-Up. Solve the equation. 3. 636 = 40 g + 28(18 – g ).

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Warm Up

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  1. Use Problem Solving Strategies and Models Warm Up Lesson Presentation Lesson Quiz

  2. Warm-Up Solve the equation. 1. 780 = 12.5r ANSWER 62.4 2. 9x + 25 = 178 17 ANSWER

  3. ANSWER 11 Warm-Up Solve the equation. 3. 636 = 40g + 28(18 – g) 4.A balloon is released from a height of 5 feet above the ground. Its altitude (in feet) after tminutes is given by the expression 5 + 82t. What is the altitude of the balloon after 6 minutes? 497 ft ANSWER

  4. High-speed Train The Acela train travels between Boston and Washington, a distance of 457miles. The trip takes 6.5 hours. What is the average speed? Rate (miles/hour) = Time (hours) Distance (miles) = r 6.5 457 Example 1 SOLUTION You can use the formula for distance traveled as a verbal model.

  5. 70.3 r ANSWER The average speed of the train is about 70.3miles per hour. 70.3miles 457 miles 6.5hours 1hour Example 1 An equation for this situation is 457 = 6.5r. Solve for r. 457 = 6.5r Write equation. Divide each side by 6.5. CHECK You can use unit analysis to check your answer.

  6. ANSWER Jet takes about 12.5hours to fly from New York to Tokyo. Guided Practice AVIATION: A jet flies at an average speed of 540miles per hour. How long will it take to fly from New York to Tokyo, a distance of 6760miles? 1.

  7. Paramotoring A paramotor is a parachute propelled by a fan-like motor. The table shows the height h of a paramotorist t minutes after beginning a descent. Find the height of the paramotorist after 7 minutes. Example 2

  8. So, the height after 7minutes is h = 2000 – 250(7) = 250 feet. ANSWER Example 2 SOLUTION The height decreases by 250feet per minute. You can use this pattern to write a verbal model for the height. An equation for the height ish = 2000 – 250t.

  9. Banners You are hanging four championship banners on a wall in your school’s gym. The banners are 8feet wide. The wall is 62feet long. There should be an equal amount of space between the ends of the wall and the banners, and between each pair of banners. How far apart should the banners be placed? Begin by drawing and labeling a diagram, as shown below. Example 3 SOLUTION

  10. x + 8 + x + 8 + x + 8 + x + 8 + x 62 = 62 5x + 32 = 5x 30 = x = 6 ANSWER The banners should be placed 6feet apart. Example 3 From the diagram, you can write and solve an equation to find x. Write equation. Combine like terms. Subtract 32 from each side. Divide each side by 5.

  11. Write a verbal model. Then write an equation. STEP 1 Example 4 SOLUTION An equation for the situation is 460 = 30g + 25(16 – g).

  12. Solve for gto find the number of gallons used on the highway. STEP 2 The correct answer is B. ANSWER 30 12 + 25(16 – 12) = 360 + 100 = 460 Example 4 460 = 30g + 25(16 – g) Write equation. 460 = 30g + 400 – 25g Distributive property 460 = 5g + 400 Combine like terms. 60 = 5g Subtract 400 from each side. 12 = g Divide each side by 5. The car used 12 gallons on the highway. CHECK:

  13. PARAMOTORING: The table shows the height h of a paramotorist after tminutes. Find the height of the paramotorist after 8 minutes. 2. So, the height after 8minutes is h = 2400 – 210(8) = 720 ft ANSWER Guided Practice

  14. ANSWER The space between the banner and walls and between each pair of banners would increase to 9.5feet. Guided Practice WHAT IF?In Example 3, how would your answer change if there were only three championship banners? 3.

  15. FUEL EFFICIENCY A truck used 28 gallons of gasoline and traveled a total distance of 428 miles. The truck’s fuel efficiency is 16miles per gallon on the highway and 12 miles per gallon in the city. How many gallons of gasoline were used in the city? 4. ANSWER Five gallons of gas were used. Guided Practice

  16. 2.5 h, or 2 h 30 min ANSWER ANSWER 12 in., 12 in., 24 in., 6 in. Lesson Quiz • If you hike at an average speed of 2.8 miles per • hour, how long will it take you to hike a trail that is • 7 miles long? • You cut a 54-inch rope into four pieces. Two of the • pieces are the same length, a third piece is twice as • long as each of the two equal pieces, and the fourth • piece is half as long as each of the two equal pieces. • Find the length of each piece.

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