Mixture and Percentage Applications

Systems of Linear Equations Lesson #6: Mixture and Percentage Applications Mixture Applications Clars Ex. #1 Cashew nuts costing $22/kg are mixed with Brazil nuts costing $16/kg. The mixture weighs 50 kg and sells for $18/kg. a) How much does it cost to buy the whole mixture? 50 (18) = 900 b) Form a system of equations and solve it to determine the number of kilograms of each type of nut used in the mixture. Let x = #kg of cashew nuts and y= #kg of Brazil nuts. x+y=50 y=50-x 22x + 16y= 900 22x+16(50-x)=100 22x+100-16x-900 6x=100 X= 52 X=16 CHECK X+Y=50 50 PS=50 LS=RS 22x+164 =900 45:16+53号 15:22(16)+16(32) = 900 25-900 LS-PS y=50-x y=50-(163) y=33 The mixture had 16 kg of cashew nuts and 338kg of Brazil nuts. Class Ex. #2 Lora invested her inheritance of $48 000 in two different mutual funds. At the end of one year one fund had earned 10.5% interest and the other fund had earned 12% interest. If she received a total of $5520 in interest, how much did she invest in each mutual fund? Let x = amount invested in 10.5% interest fund Let y = amount invested in 12% interest fund x+y=48000 48000-x 1.105x 1.12y53520, caroni 10.4% earned initial earned 110.5%=1:45 12% 12% 1.12 =48000-5520 #53520 1.1052+1.12y=53520 1.105x+1.12 (48000-x)=53520 1.105x+53760-1.12X-53520 X = 16000 CHECK X 48000 1.105x1.12 53520 LS: 16000+32000 LS: 1.105(10000) +1.12(32000) = 48000 RS: 48000 LS=RS =53520 23:53520 LS = PS y=48000-2 y=48000-(16000) -0.0152-2404-32000 She invested #16000 and $32000 in each mutual fund. 488 Systems of Linear Equations Lesson #6: Mixture and Percentage Applications Class Ex. 43 Earl the chemist has to make 180 mL of 60% hydrochloric acid (HCI) solution. He has available a one litre bottle of 45% HCI solution and a one litre bottle of 70% HCl solution by volume. How many mL of each solution are mixed to make the 60% HCl solution? Let x = # mL of 450% HCl and y= #ML of 70% HC) x+y = 180 y=180-x 0.45x +0.70.60 (180), 460% 0.6 0.45%+0.74 108 = 0.6(180) b/ that is the goul of the question. 0.45x+0.7(180-x) = 108 0.45x+126-0.7x-108 -0.25x-18 x72 y-180-x ५=180-(72) y=102 CHECE XTU 180 LS (92) (108) 180 PS: 160 LS FS 0.45210.94 108 LS: 0-45 (72) +0.7 (108) 108 PS=108 LS-RS. 72mL of 45% HCI solution and 108 mL of 70% HCl solution are mute Complete Assignment questions #1 - #8 Assignment In problems #1-#8 use the following procedure. a) Introduce variables to represent the unknown values. b) Form a system of equations involving the variables. c) Solve the system. d) Answer the problem and check the solution. 1. Candy costing $6 per kg is mixed with candy costing $4.50 per kg to produce 112 kg of candy worth $612. How many kg of each type of candy were used? Let x = # kg at $6 per kg and y=#kg at $4.50 per kg x+y=112y=112-X 6x+4.5y = 612 6x+4.5(112-x)=612 y=112-x 6x504-4.5x = 612 1.5x108 X=72 y=112-(72) y=40 CHECK: X+Y=112 6x+4.54 = 612 LS: (92)+(40) LS:6(72)+4.5 (40) = = 112 25112 LS=RS = 432-180 = 612 RS=612 LS = RS 72kg of #6 per kg candy and 40kg of $4.50 per kg candy. Systems of Linear Equations Lesson 1. Mixture and Percentage Applications 489 3 2. Chad invested of his $56 000 lottery winnings in two different mutual funds. At the 4 end of the year the Balanced Fund had earned 6.5% interest, but the Emerging Markets Fund had lost 3%. If the value of Chad's funds increased by $1 590, determine the amount invested in each fund. Let X amount invested in Balanced fund and y amount inverted in Emerging Markets Fund. ×56000=42000-1590 = 43540 x+y=42000 y=42000- "earned 6.5%=106.5% 1.065 1.065x0.97y=43590 "lost 3%"= 97% = ٥۰۹۶ 1.0652+0.97 (42000-x)=43590 1.0652-90740-0.97x43540 y=42000-x CHECK: X+Y=42000 0.095x=2850 y = 42.000-(30 800) 25: (30000)+(12000) = 42000 RS: 42000 10652-0.774 = 48590 25:1.065 (50000)+0.17 (13000) #43590 BS-43590 LSPS X-30000 y=12000 LSES $30000 invested in Balanced fund and $12000 invested in Emerging Markets fund. 3. Shoji invested $7000, part at 9% interest and part at 6% interest. The interest obtained from the 6% investment was half of the interest obtained from the 9% investment. How much was invested at each rate? Let x cmount at 9%% and 8g amount at 6% x+y=7000 7000-x andy=(0.092) CHECK x+y=7000 0.064= (0.09%) LS: 4000-8000 LS: 0.06 (3000) -7000 9 = 7000-x BS: 7000 = 180 RS: ±(0.09) (4000) = 180 LS=RS 0.06(7000-x)=±(0.09%) 4200.105x x = 4000 LS-PS 420-0.06 0.045x y=7000-(4000) y = 3000 Shoji invested $4000 at 9% and $3000 at 6% 4. 300 grams of Type A Raisin Bran is mixed with 500 grams of Type B Raisin Bran to produce a mixture which is 11% raisins. Type A Raisin Bran has twice as many raisins per kilogram as Type B. What percentage of raisins are in each type of Raisin Bran? Let x = percentage of raisins in Type A Let y percemage of raisins in Type B X=24 300x500 y 800 (11) 300x50048800 300(24)+50048800 x=2(8) 600 y+ 500 y 8800 1400 y = 8800 y=8 X=16 CHECK: 500X5004 = 8800 LS: 300(10)+500(5) = 8800 25: 8800 x=24 25:16 RS: 2(8)=16 LS = PS Type A has 16% raisins and Type B has 8% raisins.