12+-+Sec.+7.6

Solving Word Problems Using Systems of Equations 7.6 By Evelio M & Tyler R Remember that the key to writing a //verbal model//, assigning //labels//, writing and //algebraic model//, //solving// the original algebraic model, and answering the question of the original problem. Remember that you have three methods for solving the system: graphing, substitution, and linear combinations.

__Solving by Graphing__ A solution is an ordered pair that is a solution of each equation in the system. The graph of a system is the graph of all solutions of the system.

__Solve By Substitution__ To solve by substitution you need to find either the "x" or the "y" variable then plug it back into the other equation.

Ex 1) A group of friends take a day-long trip tubing down a river. The company that offers the tubing trip charges $15 to rent a tube for a person to use a and $7.50 to rent a "cooler" tube, which is used to carry food and water in a cooler. The friends spend $360 to rent a total of 26 tubes. How many of each type of tube do they rent?

x=tube, y=coolers 15x+7.50y=360 x+y=26 y=(-x+26) 15x+7.50(-x+26)=360 15x-7.50x+195=360 - 195 - 195 15x-7.50x=165 7.5x = 165 7.5 7.5 x=22 22+y=26 -22 -22 y=4

There are 22 regular tubes rented and 4 "cooler" tubes rented.  Ex 2) During a football game, the parents of the football players sell pretzels and popcorn to raise money for new uniforms. They charge $2.50 for a bag of popcorn and $2 for a pretzel. The parents collect $336 in sales during the game. They sell twice as many bags of popcorn as they do pretzels. How many bags of popcorn do they sell? How many pretzels do they sell?

X=Popcorn, Y=Pretzels 2.50x+2y=336 x=2y 2.50(2y)+2y==336 7y=336 divide by 7 on both sides y=48 Plug 48 in for y in the equation x = 2y, so x = 2(48) x=96 There are 96 bags of popcorn sold and 48 pretzels sold.  Ex 3) Five hundred gallons of 82-octane gasoline is obtained by mixing 80-octane gasoline with 86-octane gasoline. How much of each must be used?

x=80 octane y= 86 octane x+y=500 80x+86y=500*82 y=(-x+500) 80x+86(-x+500)=500*82 80x-86x+43000=41000 -41000 -41000 80x-86x=-2000 -6x=-2000 -6 -6 x=333.3 To find what y =, plug in x = 333 (1/3) into the equation x + y = 500. So 333 (1/3) + y = 500 means that y = 166 and 2/3. To get 82 octane gas, 333 and 1/3 gallons of 80-octane gas and 166 and 2/3 gallons of 86-octane gas must be mixed. __Practice Problems Weblink__  This link will take you to a website with more practice problems. Practice Problems

Practice Problems An exam worth 145 points contains 50 questions. Some of the questions are worth two points and some are worth five points. How many two point questions are on the test? How many five point questions are on the test?
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You have 50 tickets to ride the Ferris wheel and the roller coaster. If you ride 12 total rides, using 3 tickets fo each Ferris wheel ride and 5 tickets for each roller coaster ride, how many times did you go on each ride?
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