Equations and Problem Solving

1. Equations and Problem Solving ALGEBRA 1 LESSON 4-8 (For help, go to Lesson 1-1.) Write a variable expression for each situation. 1. value in cents of q quarters 2. twice the length 3. number of miles traveled at 34 mi/h in h hours 4. weight of 5 crates if each crate weighs x kilograms 5. cost of n items at $3.99 per item 4-8

2. Equations and Problem Solving ALGEBRA 1 LESSON 4-8 Solutions 1. value in cents of q quarters: 25q 2. twice the length : 2 3. number of miles traveled at 34 mi/h in h hours: 34h 4. weight of 5 crates if each crate weighs x kilograms: 5x 5. cost of n items at $3.99 per item: 3.99n 4-8

3. Define: Let t = the time the airplane travels. Then t – 1 = the time the jet travels. Aircraft Rate Time Distance Traveled Airplane 180 t 180t Jet 330 t – 1 330(t – 1) Equations and Problem Solving ALGEBRA 1 LESSON 4-8 An airplane left an airport flying at 180 mi/h. A jet that flies at 330 mi/h left 1 hour later. The jet follows the same route as the airplane on parallel altitudes. How many hours will it take the jet to catch up with the airplane? 4-8

4. Relate: distance traveled equals distance traveled by airplane by jet Write: 180 t = 330( t – 1 ) 180t – 330t = 330t – 330 – 330tSubtract 330t from each side. –150t = –330Combine like terms. –150t –150 –330 –150 = Divide each side by –150. 1 5 t = 2Simplify. 1 5 t – 1 = 1 1 5 The jet will catch up with the airplane in 1 h. Equations and Problem Solving ALGEBRA 1 LESSON 4-8 (continued) 180t = 330(t – 1) 180t = 330t – 330 Use the Distributive Property. 4-8

5. Define: Let x = time of trip uphill. Then 3 – x = time of trip downhill. Relate: distance uphill equals distance downhill Part of hike Rate Time Distance hiked Uphill 4 x 4x Downhill 6 3 – x 6(3 – x) Write: 4 x = 6( 3 – x ) Equations and Problem Solving ALGEBRA 1 LESSON 4-8 Suppose you hike up a hill at 4 km/h. You hike back down at 6 km/h. Your hiking trip took 3 hours. How long was your trip up the hill? 4-8

6. 4x + 6x = 18 – 6x + 6xAdd 6x to each side. 10x = 18 Combine like terms. = Divide each side by 10. 10x 10 18 10 4 5 x = 1 Simplify. Your trip uphill was 1 h long. 4 5 Equations and Problem Solving ALGEBRA 1 LESSON 4-8 (continued) 4x = 6(3 – x) 4x = 18 – 6xUse the Distributive Property. 4-8

7. Define: Let x = the speed of the jet flying east. Then x + 50 = the speed of the jet flying west. Relate: eastbound jet’s plus westbound jet’s equals the total distance distance distance Jet Rate Time Distance Traveled Eastbound x 2 2x Westbound x + 50 2 2(x + 50) Write: 2 x + 2( x + 50 ) = 2500 Equations and Problem Solving ALGEBRA 1 LESSON 4-8 Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 50 mi/h faster than the other. After 2 hours, they are 2500 miles apart. Find the speed of each jet. 4-8

8. 2x + 2(x + 50) = 2500 2x + 2x + 100 = 2500 Use the Distributive Property. 4x 4 2400 4 = Divide each side by 4. x = 600x + 50 = 650 Equations and Problem Solving ALGEBRA 1 LESSON 4-8 (continued) 4x + 100 = 2500 Combine like terms. 4x + 100 – 100 = 2500 – 100Subtract 100 from each side. 4x = 2400 Simplify. The jet flying east is flying at 600 mi/h. The jet flying west is flying at 650 mi/h. 4-8

9. Equations and Problem Solving ALGEBRA 1 LESSON 4-8 1. The sum of three consecutive integers is 117. Find the integers. 2. You and your brother started biking at noon from places that are 52 mi apart. You rode toward each other and met at 2:00 p.m. Your brother’s average speed was 4 mi/h faster than your average speed. Find both speeds. 3. Joan ran from her home to the lake at 8 mi/h. She ran back home at 6 mi/h. Her total running time was 32 minutes. How much time did it take Joan to run from her home to the lake? 38, 39, 40 your speed: 11 mi/h; brother’s speed: 15 mi/h about 13.7 minutes 4-8