Section 7 – 4 Systems of Linear Equations (Word Problems) Objective: To write and solve systems of linear equations.

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Section 7 – 4 Systems of Linear Equations (Word Problems) Objective: To write and solve systems of linear equations

Methods for Solving Systems of Linear Equations Graphing: Substitution: Elimination: Use for systems that will graph easily. Use when one equation can be or is solved for one of the variables. Use for any system.

A)Your community center sells a total of 292 tickets for a basketball game. An adult ticket costs $3. A student ticket costs $1. The sponsors collect $470 in ticket sales. Write and solve a system to find the number of each type of ticket sold.

B)The freshman class sells a total of 64 tickets to a play. A student ticket costs $1 and an adult ticket costs $2.50. Your class collects $109 in total ticket sales. How many adult tickets did you sell? How many student tickets did you sell?

C)Suppose the Junior Class sells gift wrap for $4 per package and greeting cards for $10 per package. Your class sells 205 packages in all and receives a total of $1084. Find the number of packages of gift wrap and the number of packages of greeting cards sold.

D)Suppose the band sells bags of popcorn for $5 per bag and bags of mixed nuts for $8 per bag. The band sells a total of 240 bags and receives a total of $1614. Find the number of bags of popcorn and the number of bags of mixed nuts sold.

Rate x Time = Distance Airspeed + Tailwind = Rate Airspeed – Headwind = Rate

A)Suppose you fly from Miami, Florida, to San Francisco, California, It takes 6.5 hours to fly 2600 miles again a head wind. At the same time, your friend flies from San Francisco to Miami. Her plane travels at the same average airspeed, but her flight only takes 5.2 hours. Find the average airspeed of the planes. Find the average wind speed.

B)A plane takes about 6 hours to fly 2400 miles from New York City to Seattle, Washington. At the same time, your friend flies from Seattle to New York City. His plane travels with the same average airspeed, but his flight takes 5 hours. Find the average airspeed of the planes. Find the average wind speed.

C)A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back took 14 hours. What is the speed of the boat in still water? What is the speed of the current?

C)A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages 2.75 mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relative to the riverbank. Find the family’s paddling speed in still water and the speed of the current of the river.

Homework: Practice Questions From Homework AGAIN! Be familiar with the different types of problems that can be modeled by a system of equations.