(For help, go to Lesson 1-1.) ALGEBRA 1 LESSON 2-5 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 Equations and Problem Solving 2-5

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 Equations and Problem Solving ALGEBRA 1 LESSON

The width of a rectangle is 3 in. less than its length. The perimeter of the rectangle is 26 in. What is the width of the rectangle? Relate: The width is 3 in. less than the length. Then x – 3 = the width. Define: Let x = the length. The width is described in terms of the length. So define a variable for the length first. Write: P = 2 + 2wUse the perimeter formula. 26=2 x + 2( x – 3 ) Substitute 26 for P, x for and (x – 3) for w. Equations and Problem Solving ALGEBRA 1 LESSON

The sum of three consecutive integers is 72. Find the integers. Relate: first plus second plus third is 72 integer integer integer Define: Let x = the first integer. Then x + 1 = the second integer, and x + 2 = the third integer. Write: x + x x + 2 = 72 Equations and Problem Solving ALGEBRA 1 LESSON

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? AircraftRateTimeDistance Traveled Airplane180t180t Jet330t – 1330(t – 1) Define:Let t = the time the airplane travels. Then t – 1 = the time the jet travels. Equations and Problem Solving ALGEBRA 1 LESSON

Relate:distance traveledequalsdistance traveled by airplaneby jet Write the equation: 180t = 330( t – 1 ). Equations and Problem Solving ALGEBRA 1 LESSON (continued)

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? Define:Let x = time of trip uphill. Then 3 – x = time of trip downhill. Relate: distance uphillequals distance downhill Part of hikeRateTimeDistance hiked Uphill4x4x Downhill63 – x6(3 – x) Write the equation: 4x = 6(3 – x ) Equations and Problem Solving ALGEBRA 1 LESSON

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. Define:Let x = the speed of the jet flying east. Write the equation: 2 x + 2( x + 50 ) = 2500 Then x + 50 = the speed of the jet flying west. Relate:eastbound jet’s plus westbound jet’s equals the total distance distance distance JetRateTimeDistance Traveled Eastboundx22x Westboundx (x + 50) Equations and Problem Solving ALGEBRA 1 LESSON

1.The sum of three consecutive integers is 117. Write an equation that represents the problem. 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. Write an equation that represents the problem. 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. Write an equation that represents the problem. X + (x+1) + (x + 2) = v + 2 (v + 4) = 52 8t = 6(32 – t) Equations and Problem Solving ALGEBRA 1 LESSON