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Applications of Linear Systems 1. It costs $11.46 for 4 hamburgers and 6 milkshakes and $2.47 for 2 hamburgers and 1 milkshake. Determine the cost of 1 hamburger and 1 milkshake. It costs $11.46 for 4 hamburgers and 6 milkshakes and $2.47 for 2 hamburgers and 1 milkshake. Determine the cost of 1 hamburger and 1 milkshake. h= cost of a hamburger m = cost of a milkshake 4h + 6m = $11.46 2h + m = $2.47 8h + 12m = $22.92 -8h -4m = - 9.88 8m = $13.04 m = $1.63, 2h + 1.63 = 2.47, 2h = 0.84 h=$0.42 (0.42, 1.63) check 4(0.42) + 6(1.63) = 11.46 1.68 + 9.78 = 11.46 11.46=11.46 page 198 # 1 The width of a rectangles is 14 inches less than the length. The perimeter of the rectangle is 92 inches. Define the two variables and write two equations. The width of a rectangles is 14 inches less than the length. The perimeter of the rectangle is 92 inches. Define the two variables and write two equations. w = width l = length w=l – 14 2w + 2l = 92 page 198 # 2 - SOLVE The price of a sweater is $5 less than twice the price of a shirt. If four sweaters and three shirts costs $200, find the price of each shirt and each sweater. The price of a sweater is $5 less than twice the price of a shirt. If four sweaters and three shirts costs $200, find the price of each shirt and each sweater. a = price of sweater b = price of shirt a = 2b - 5 4a + 3b = 200 4(2b-5) + 3b = 200 8b – 20 + 3b = 200 11b – 20 = 200 11b = 220 b = 20, a = 2(20) – 5 = 35 (35,20) 4(35) + 3(20) = 200 140 + 60 =200 page 199 A shipment of TV sets contains some weighing 30 kg each and the others weighing 50 kg each. The total weight of the shipment is 880 kg. If there are 20 TV sets all together, how many weigh 50 kg? Page 200 #1 and # 2 The cost of eight pineapple toppings for frozen yogurt and three strawberry toppings costs $22. Four pineapple toppings and 7 strawberry toppings also costs $22. Find the price of each kind of topping. Two kinds of candy were combined to make 50 pounds of mixture. The less expensive candy costs 37 cents per pound and the more expensive candy costs 45 cents per pound. If the total mixture was worth 40 cents per pound, how many pounds of each candy were used. The cost of eight pineapple toppings for frozen yogurt and three strawberry toppings costs $22. Four pineapple toppings and 7 strawberry toppings also costs $22. Find the price of each kind of topping. p= cost of pineapple toppings s = cost of strawberry toppings 8p + 3s = 22 4p + 7s = 22 8p + 3s = 22 -8p – 14s = -44 - 11s = -22 s = 2 8p + 3(2) = 22 8p = 16 p =2 (2,2) 4(2) + 7(2) = 22 8 + 14 = 22 22=22 Two kinds of candy were combined to make 50 pounds of mixture. The less expensive candy costs 37 cents per pound and the more expensive candy costs 45 cents per pound. If the total mixture was worth 40 cents per pound, how many pounds of each candy were used. x = number of pounds of 37 cent candy y = number of pounds of 45 cent candy x + y = 50 (total number of pounds) .37x + .45y = .40(50) (total cost of mixture) 37x + 45y = 2000 ( multiply by 100 to eliminate decimal) -37x – 37y = -1850 (multiply 1st equation by -37) 8y = 150 y=18.75 x + 18.75 = 50 x =31.25 (31.25, 18.75) .37(31.25) + .45(18.75) = 20 11.5625+8.4375 =20 Upstream/Downstream page 201 upstream = against the current boat goes slower downstream = with the current boat goes faster With the wind (tailwind) = plane is pushed by the wind and goes faster Against the wind (headwind) = plane flies into the wind and goes slower A motorboat traveling with the current (downstream) can go 100 mile in 4 hours. Against the current (upstream), it takes 5 hours to go the same distance. Find the rate of the motorboat in still water and the rate of the current. speed (rate) time distance upstream x-y 5 100 downstream x+y 4 100 or define the variables Let x= speed of boat in still water Let y = speed of current 5(x-y)=100 4(x+y)=100 solve and check x-y=20 x+y=25 ---------- 2x=45 x=22.5 22.5-y=20 y=2.5 (22.5,2.5) 22.5+2.5=25 25=25 The speed of the boat is 22.5 miles per hour the speed of the current is 2.5 miles Homework • Page 202, 204, 205, 206, 207

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