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The Mixture Project

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luz aguilar

on 13 December 2012

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Transcript of The Mixture Project

The Mixture Project By: Luz Aguilar Anh Nguyen Kailana Negrete Samantha Rodriguez Rocio Medina Margret Tapia Mr.Nguyen 6th period Candy worth 1.25 a pound was mixed with candy worth 1.50 a pound to produce a mixture worth 1.35 a pound.How many pounds of each mixture were used to make 45 pounds of the mixture? A 3% solution of sulfric acid was mixed with an 18% solution of sulfric acid to produce an 8% solution.How much 3% solution and how much 18% solution were used to produce 15L of 8% solution? Jake has $4,000 invested at 8% annual interest.He has $2800 more to invest.At what rate must he invest the $2800 to have a total annual interest of $628? The sum of 4 times Lisa's age and 7 times Jane's age is 169.Jane is 1 year more than twice as old as Lisa is.Find each of their ages. The perimeter of a rectangle is 66cm.The length of the rectangle is 1cm more than three times the width.Find the dimensions of the rectangle. The ten digit number of a certain two-digit number is 1 more than 3 times the unit digit.The original number is 9 less than 3 times the number formed by interchanging the digits.Find the original number. The McLeans drove from the house to Dayton at 75mi/h.When they returned,the traffic was heavier and they drove at 50mi/h.If it took them 1 hour longer to return than to go,how long did it take them to drive home? A ship travels from New York to Southampton,England at 33 miles per hour.A plane traveling 605 miles per hour takes 104 hours less time to make the same trip.How far apart are the two cities? Joe flew his small plane 900 miles in 5 hours with the wind.He flew 700 miles against the wind in 7 hours.Find the rate at which he flew in still air and the rate of the wind. The cost of 4 chairs and 15 chairs is $904.80.The cost of 2 tables and 10 chairs is $549.90.Find the cost of each table and each chair. 66=6w+2+2w 66=8w+2 64=8w 8 8 8cm=w add like terms divide 8 to both sides check your work 66=6*8+2+2*8 66=48+2+16 66=66 2L+2w=66 2L+16=66 2L=50 subtract 16 to both sides subtitute w for 8 and multiply w=width L=length L=25cm divide 2 to both sides 2 2 2L+2w=66 2*25+2*8=66 subsitute L for 25 and w for 8 and solve 66=66 w=8cm L=25cm x=pounds of $1.25 candy y=pounds of $1.50 candy x+y=45 1.25x+1.50y=60.75 multiply the second equation by 100 to clear decimals (1.25*100)+(1.50*100)=(60.75*100) x+y=45 125x+150y=6075 multiply the first equation by 125 & subtract it from the second x+y=45 125x+125y=5625 125x+150y=6075 125x+125y=5625 25y=450 divide both sides by 25 25 25 y=18 subtitute y for 18 into one of the equations and solve for x x+18=45 -18 -18 x=27 you need 18 pounds of the $1.25 candy and 27 pounds of the $1.50 candy 18+27=45 check your work D=R*T 900=R*5hrs (with the wind) 5 5 =180mi/h 700=R*7hrs 7 7 (against the wind) x=speed of plane in still air y=speed of the wind x+y=180 x-y=100 =100mi/h {first find x} subtract 180 & 100 - 2x=280 2 2 divide 2 to both sides x=140 replace x for 140 into one of the equations and solve 140+y=180 -140 -140 y=40mi/h x=140mi/h y=40mi/h 140+40=180 check your work t=tables c=chairs 4t+15c=904.80 2(2t+10c=549.90) 4t+15c=904.80 4t+20c=109.80 -5c=-195 c=$39 2t+10.39=549.90 2t+390=549.90 2t+390=159.90 t=79.95 check work 4t+15c=904.80 319.80 585 4(79.95)+15(39)=904.890 + =904.80 x=unit's digit y=ten's digit=3x+1 original number: 10y+x=10(3x+1)=30x+10 interchanged number: 10x+y=10x+3x+1=13x+1 30x+10=3(13x+1)-9=39x+3-9=39x-6 9x=16 x=2 y=3x+1=7 the original number is:72 L=lisa's age J=jane's age 4L+7J=169 J=2L+1 ------>rewritten:2L-J=-1 use the elimination process but first multiply by the 2nd equation by 2 you get: 4L+7J=169 4L-2J=-2 subtract equation one and two 9J=171 9 9 divide 9 to both sides J=19 J=2L+1 becomes 19=2L+1 18=2L L=9 divide 2 to both sides x=3% solution of sulfric acid y=18% solution of sulfric acid 3(x+y=15) 100(0.03x+0.18y=8(15)) 3x+18y=120 3x+3y=45 15y=75 15 15 =5 x=7L y=5L 4L+7J=169 check your work 4(9)+7(19)=169 36+133=169
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