Watch the below videos for slow lessons on the Elimination Method Elimination Method Video-1Elimination Method Video-2 now for your homework answers Writing Systems to Model Situations ------------------------------------- 1: The admission fee at a carnival is $3.00 for children and $5.00 for adults. On the first day, 1,500 people entered the fair and $5,740 was collected. How many children and adults went to the carnival? Pick meaningful variable names : A for number of adults who went C for number of children who went what you know so far.... 3C + 5A = 5740 what the total amount of tickets cost C + A = 1500 number of children and adults who went now let's solve it.... I want to get rid of Cs first, I could get rid of As first, but in this case, I picked Cs I got 3C in the first row, so if I multiply the second row by -3...to make sure I create a -3C so the Cs in both rows add to 0 so I did -3( C + A = 1500 ) to get -3c -3C = -4500 3C + 5A = 5740 -3C - 3A = -4500 ------------------------------------- 2A = 1240 A = 620 now plug A back into the equation A + C = 1500 A + C = 1500 620 + C = 1500 -620 -620 ------------------------ C = 880 So ( adults , children ) is ( 620 , 880 ) 2: A builder placed two orders with a hardware store. a: The first order was for 25 sheets of plywood and 4 boxes of nails and the total bill was $357. b: The second order was for 35 sheets of plywood and 2 boxes of nails and the bill totaled $471. What were the prices of one piece of plywood and one box of nails? Label your variables first!!!! N # of nails P # of pieces of plywood 25P + 4B = 357 35P + 2B = 471 removing the Bs first is easier, so lets create -4b to get rid of +4b -2( 35P + 2B = 471 ) is -70P - 4B = -942 25P + 4B = 357 -70P - 4B = -942 -------------------------- -45P = -585 -45P = -585 ----- ------ -45 -45 P = 13 plug P into the top equation 25P + 4B = 357 25(13) + 4B = 357 325 + 4B = 357 -325 -325 -------------------- 4B = 32 B = 8 3: Two friends bought some markers and pens. M # of markers P # of pens a: The first bought 4 markers and 5 pens and it cost him $6.71. 4M + 5P = 6.71 b: the second friend bought 5 markers and 3 pens, which cost her $7.12. 5M + 3P = 7.12 these are our two equations question is, do we get rid of M or P first?....actually doesn't matter let's get rid of P first -3( 4M + 5P = 6.71 ) 5( 5M + 3P = 7.12 ) -12M - 15P = -20.13 25M + 15P = 35.60 ---------------------------- 13M = 15.47 M = 1.19 plug M into either equation to find P 5(1.19) + 3P = 7.12 5.95 + 3P = 7.12 -5.95 = -5.95 ----------------------- 3P = 1.17 P = 0.39 Pens = 0.39 Markers = 1.19 ( 0.39 , 1.19 ) 4. The ticket price for the movies is $7.50 for children and $10.50 for adults. One night 825 people bought tickets and $8005.50 was collected from tickets sales. How many children and adults bought tickets? Label A for # of adults and C for # of children a: A + C = 825 10.50A + 7.50C = 8005.50 ----------------------------------- this is going to get real messy...so don't get concerned about it -7.50( A + C = 825 ) I want to get rid of the C first -7.50A - 7.50C = -6187.50 -7.50A - 7.50C = -6187.50 10.50A + 7.50C = 8005.50 ----------------------------------- 3A = 1818 A = 606 now plug P back into the first equation A + C = 825 606 + C = 825 -606 -606 ----------------------- C = 219 Adults = 606 Children = 219 ================================================================================ Restaurant Menu Problems _______________________________ 5: The Smith family orders two chicken burritos and three steak burritos. These contain 3460 calories. The Grant family orders three chicken burritos and two steak burritos. These contain 3340 calories. Find the number of calories in each chicken burrito and in each steak burrito. Justify your answer. First ==>> label your variables C # chicken burritos S # steak burritos Second express your two equations 2C + 3S = 3460 3C + 2S = 3340 do I get rid of C or S first..?..doesn't matter..either choice works so I pick C..... but how..? 2C + 3C don't add to 0, I need them to add to 0 to get rid of C so I pull this trick -3( 2C ) + 2( 3C ) = -6C + 6C = 0 so I multiply the top equation by -3 and the bottom equation by 2 -3( 2C + 3S = 3460 ) 2( 3C + 2S = 3340 ) which turns into -6C - 9S = -10380 +6C + 4S = 6680 ---------------------- -5S = -3700 ---- ----- -5 -5 S = 740 now plug S=740 back into one of the original equations, doesn't matter which one 2C + 3S = 3460 2C + 3(740) = 3460 2C + 2220 = 3460 - 2220 -2220 --------------------- 2C = 1240 ---- ------ 2 2 C = 620 6: The Smith family orders four sides of chips and four sides of beans. These contain 1980 calories. The Grant family orders two sides of chips and five sides of beans. These contain 1350 calories. Find the number of calories in each side of ships and number of calories in each side of beans. Justify your answer. First label your variables ==>> C for chips B for beans Second express your equations 4C + 4B = 1980 2C + 5B = 1350 lets get rid of C first create -4C from the bottom equation..multiply it by -2 4C + 4B = 1980 -2( 2C + 5B = 1350 ) which becomes 4C + 4B = 1980 -4C -10B = -2700 ------------------------- -6B = -720 ----- ------ -6 -6 B = 120 plug B back into the top equation to get C 4C + 4B = 1980 4C + 4(120) = 1980 4C + 480 = 1980 - 480 = -480 ------------------------- 4C = 1500 4C = 1500 ---- ------ 4 4 C = 375 7: The Smith family orders three iced teas and three juice drinks which contain 1260 calories. Label variables first T : ice tea J : juice 3T + 3J = 1260 ( 1st equation ) The Grant family orders one ice tea and 4 juice drinks, total calories of 1140. 1T + 4J = 1140 ( 2nd equation ) let's get rid of T first, so multiply the 2nd equation by -3 to create -3T 3T + 3J = 1260 ==>> 3T + 3J = 1260 -3( 1T + 4J = 1140 ) ==>> -3T -12J = -3420 --------------------------- ------------------- -9J = -2160 ---- ------- -9 -9 J = 240 3T + 3J = 1260 3T + 3(240) = 1260 3T + 720 = 1260 - 720 -720 --------------------- 3T = 540 ---- ----- 3 3 T = 180 plug J=240 back in the first equation