Algebra 1: Problem Set 6R Systems of Equations ... - MathChamber

**Algebra** 1: **Problem** **Set** **6R****Systems** **of** **Equations** REVIEWThe Good, the Bad, and the UGLY!Name________________________________________Date ________________________ Period ________For the following problems, EXPLICITLY DEFINE YOUR VARIABLESCREATE a system **of** equations and SOLVE.1. The sum **of** two numbers is 16. Their difference is 20. What are the numbers?2. An airplane travels 1560 miles in 3 hours flying with the wind (i.e. a “tail-wind”). Thereturn trip, against the wind (i.e. a “head-wind”), takes 4 hours. Assume that the windspeed (measured in miles per hour) has the same force and direction for each trip.Find the average rate **of** speed **of** the plane in still air.Hint: Define the “still air” speed **of** the plane and the wind speed as separatevariables.

3. How many pounds **of** cashew nuts that sell for $2 pound should be mixed with peanuts,which sell for 80¢ a pound, to make a 10-pound mixture that sells for $1.28 a pound?4. The value **of** a two-digit number is 12 times its tens digit. The sum **of** the digits is 12.What is the number?(Hint: You’ll have to apply your knowledge **of** PLACE VALUE. THINK – what is theVALUE **of** the ten’s digit??)5. A company is going to mix two kinds **of** c**of**fee. The Mountain Grown variety kindcosts $7 per pound. The Valley Sown variety costs $4 per pound. The company wants90 pound mix worth $6 per pound. How much **of** the Mountain Grown variety kindshould it use?

6. An art museum has a general admission rate **of** $5, but students pay $3. Yesterday, themuseum collected a total **of** $902 from 216 people. How many general admissioncustomers attended the museum?7. A boat can travel upstream (against the current) 60 miles in 6 hours. The boat cantravel downstream (with the current) the same distance in 5 hours. What is the rate **of**the current?Hint: Define the still-water speed **of** the boat and the speed **of** the current as separatevariables.

8. SOLVING SYSTEMS OF EQUATIONS – REVIEWTHE GOOD, THE BAD, AND…Graph each **of** the following six equations on the coordinate plane provided belowA) 2x− y = −2B)1y = − x + 82C) x = −3D) x + 2y= −4E)1y = x + 23F) y = 2x− 2Copy each problem below into your notebook and solve.Based on equations A thru F above, use either algebraic method,SUBSTITUTION or ELIMINATION, to find the solution for:1) A & B2) A & C3) A & D4) A & F5) C & E6) B & E7) D& E… THE UGLY!!Verify that your algebraic solutions match your graphical solutions.