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# Recent problems solved by 'Maths68'

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 Functions/516389: For each function, find f(-2), f(-1/2), f(3), and f(7). 1. f(x)= -1/3x + 11 solutions Answer 344355 by Maths68(1474)   on 2011-10-17 13:21:08 (Show Source): You can put this solution on YOUR website!For each function, find f(-2), f(-1/2), f(3), and f(7). f(x)= -1/3x + 1 f(-2)=-1/3(-2)+1 f(-2)=1/6+1 f(-2)=(1+6)/6 f(-2)=7/6 f(x)= -1/3x + 1 f(-1/2)=-1/(3(1/-2))+1 f(-1/2)=-1/(3/-2)+1 f(-1/2)=2/3+1 f(-1/2)=(2+3)/3 f(-1/2)=5/3 f(x)= -1/3x + 1 f(3)=-1/3(3)+1 f(3)=-1/9+1 f(3)=(-1+9)/9 f(3)=8/9 f(x)= -1/3x + 1 f(7)=-1/3(7)+1 f(7)=-1/21+1 f(7)=(-1+21)/21 f(7)=20/21
 test/516388: What number is 62% of 251 solutions Answer 344354 by Maths68(1474)   on 2011-10-17 13:11:44 (Show Source): You can put this solution on YOUR website!What number is 62% of 25 =62% * 25 =62/100 * 25 =62/4 =15.5 15.5 is 62% of 25
 Mixture_Word_Problems/516387: A metallurgist has one alloy containing 25% copper and another containing 62% copper. How many pounds of each alloy must he use to make 45 pounds of a third alloy containing 34% copper?1 solutions Answer 344353 by Maths68(1474)   on 2011-10-17 13:09:29 (Show Source): You can put this solution on YOUR website!Ally A Amount = x Concentration = 25%=0.25 ================================================================================ Alloy B Amount = 45-x pounds Concentration = 62%=0.62 ================================================================================ Resultant Alloy Amount=45 Concentration=34%=0.34 ================================================================================ (Amount of A * Concentration of A)+(Amount of B * Concentration of B) = (Amount of Resultant * Concentration of Resultant) (x*0.25)+(45-x)(0.62)=(45)*0.34 0.25x+27.9-0.62x=15.3 -0.37x=15.3-27.9 -0.37x=-12.6 -0.37x/-0.37=-12.6/-0.37 x=34.05 pounds ============================ Ally A Amount = 34.04 pounds Concentration = 25%=0.25 ================================================================================ Alloy B Amount = 45-x=45-34.04=10.95 pounds Concentration = 62%=0.62
 Money_Word_Problems/516338: find the total cost of an engagement ring at 3240 including sale tax of 6.5%? 1 solutions Answer 344352 by Maths68(1474)   on 2011-10-17 12:52:51 (Show Source): You can put this solution on YOUR website!find the total cost of an engagement ring at 3240 including sale tax of 6.5%? 6.5% of 3240 = 3240*6.5%=3240*(6.5/100)=3240*0.065=210.6 Total cost = 3240+210.6=3450.60 or find 106.5% of 3240 = 3240*(106.5/100)=3240*1.065=3450.6
 Mixture_Word_Problems/516357: a chemist has a 10 ml of a 30% acid solution. how many millilters of pure acid must be added to obtain a 50% solution?1 solutions Answer 344351 by Maths68(1474)   on 2011-10-17 12:44:04 (Show Source): You can put this solution on YOUR website!Soluton A Amount = 10 ml Concentration = 30%=0.3 ================================================================================ Solution B Amount = x ml Concentration = 100%=1 (Pure acid) ================================================================================ Resultant Solution Amount=10+x ml Concentration=50%=0.5 ================================================================================ (Amount of A * Concentration of A)+(Amount of B * Concentration of B) = (Amount of Resultant * Concentration of Resultant) (10*0.3)+(x*1)=(10+x)*0.50 3+x=5+0.5x x-0.5x=5-3 0.5x=2 0.5x/0.5=2/0.5 x=4 ml ================================================================================ 10 ml of a 30% acid solution and 4 ml of pure acid must be mixed to obtain 14 ml of 50% solution
 Linear-equations/516377: Not sure how to find the slope of the line joining (3, 12) and (15, -2)as a fraction in the simplest form.1 solutions Answer 344350 by Maths68(1474)   on 2011-10-17 12:29:52 (Show Source): You can put this solution on YOUR website!(3, 12) and (15, -2) Slope of line = Change in y / change in x m=y2-y1/x2-x1 m=-2-12/15-3 m=-14/12 m=-7/6 Slope = -7/6
 Linear-equations/516363: write an equation in slope-intercept form for a line that passes through the given point and is parallel to the given line y=5x;(2,-1)1 solutions Answer 344349 by Maths68(1474)   on 2011-10-17 12:24:55 (Show Source): You can put this solution on YOUR website!Standard Form of Equation of the line: y=mx+b Given line y=5x Compare above equation with the standard form equation Slope = m=5 and y-intercept = b=0 Since parallel lines have same slope so slope of the required line will be:- m=5 Now we have a point(2,-1) and slope (5)of the line we can easily find required lines by putting these values in the equation of the straight line poin-slope form. m=(y2-y1)/(x2-x1) 5=(y-(-1))/(x-2) 5=(y+1)/(x-2) 5(x-2)=y+1 5x-10=y+1 y+1=5x-10 y=5x-10-1 y=5x-11 Above equation is the required equation of the line that is parallel to y=5x and contains (2,-1)
 Mixture_Word_Problems/516359: a chemist has two solutions of h2so4. one has 40% concentration and the other has a 25% concentration. how many liters of solution must be mixed to obtain 96 liters of a 27% solution1 solutions Answer 344347 by Maths68(1474)   on 2011-10-17 12:10:12 (Show Source): You can put this solution on YOUR website!Soluton A Amount = x Concentration = 40%=0.4 ================================================================================ Solution B Amount = 96-x liters Concentration = 25%=0.25 ================================================================================ Resultant Solution Amount=96 Concentration=27%=0.27 ================================================================================ (Amount of A * Concentration of A)+(Amount of B * Concentration of B) = (Amount of Resultant * Concentration of Resultant) (x*0.4)+(96-x)(0.25)=(96)*0.27 0.4x+24-0.25x=25.92 0.15x=25.92-24 0.15x=1.92 0.15x/0.65=1.92/0.15 x=12.8 liters ================================================================================ Soluton A Amount = x = 12.8 liters Concentration = 40%=0.4 ================================================================================ Solution B Amount = 96-x=96-12.8=83.2 liters Concentration = 25%=0.25 =============================================================================== 12.8 liters of 40% concentration and 83.2 liters of 25% concentration solutoins must be mixed to obtain 96 liters of a 27% solution
 Travel_Word_Problems/516340: Two buses leave Dallas at the same time and travel in opposite directions. One bus travels at 58 mph and the other travels at 52mph when will they be 363 miles apart? 1 solutions Answer 344345 by Maths68(1474)   on 2011-10-17 11:49:04 (Show Source): You can put this solution on YOUR website!Bus A Data ========== Speed = 58mph Time=t hour Distance Covered by Bus A=58*t ============= Bus B Data ============ Speed = 52mph Time=t hour Distance covered by Bus B=52*t Distance Covered by Bus A + Distance Covered by Bus B = Total Distnace apart 52t+58t=363 110t=363 110t/110=363/110 t=3.3 hour They will be 363 miles apart after 3.3 hours or 3 hours 18 minutes. Check ============= Bus A Data ========== Speed = 58mph Time=3.3 hours Distance Covered by Bus A=58*3.3=191.4 miles Bus B Data ============ Speed = 52mph Time=3.3 hours Distance covered by Bus B=52*3.3 = 171.6 miles Total Distance between two Buses = 191.4+171.6 = 363 miles
 Travel_Word_Problems/516334: A car left seattle traveling 45mph. A second car left from the same place one hour later on the same road traveling 60mph. How long will it take the second car to catch up with the first car. Which of these is the correct second eqaution for the problem?1 solutions Answer 344341 by Maths68(1474)   on 2011-10-17 11:22:35 (Show Source): You can put this solution on YOUR website!A car left seattle traveling 45mph. A second car left from the same place one hour later on the same road traveling 60mph. How long will it take the second car to catch up with the first car. Which of these is the correct second eqaution for the problem? Car A Data ========== Speed = 45mph Time = t hour Distance covered = x miles Distance = speed*time x=45*t x=45t.............(1) Car B Data ========== Speed = 60mph Time =t-1(hour) Distance covered = x Distance = Speed * time x=60*(t-1) Both cars will cover same distance 45t=60*(t-1) 45t=60t-60 45t-60t=60 -15t=-60 -15t/-15=-60/-15 t=4 hours Car A travel time 4 hours and Car B travel time 3 hours. After 3 hours of leaving same place Car B will catch Car A Check ======== Car A Data ========== Speed = 45mph Time = 4 hour Distance covered = x miles Distance = speed*time x=45*4 x=180 miles Car B Data ========== Speed = 60mph Time =t-1=4-1=3(hour) Distance covered = x Distance = Speed * time x=60*3 x=180 miles
 Proportions/516265: Two numbers are in ratio of 7:11. If 7 is added to each of the number, the ratio becomes 2:3. Find the numbers.1 solutions Answer 344313 by Maths68(1474)   on 2011-10-17 05:27:28 (Show Source): You can put this solution on YOUR website!Let x and y are two numbers x:y=7:11 x/y=7/11 11x=7y x=7y/11............(1) (x+7):(y+7)=2:3 (x+7)/(y+7)=2/3 3(x+7)=2(y+7) 3x+21=2y+14 3x=2y+14-21 3x=2y-7............(2) Put the value of x in (2) from (1) 3(7y/11)=2y-7 21y/11=2y-7 21y=11*(2y-7) 21y=22y-77 21y-22y=-77 -y=-77 y=77 Put the value of y in (1) x=7y/11............(1) x=7(77)/11 x=7*7 x=49 Numbers are 49 and 77 49/77=7/11=7:11 (49+7)/(77+7)=56/84=28/42=14/21=2/3=2:3
 Graphs/516236: How do I solve 0.3x-0.2y=4 and 0.2x + 0.3y=29/19 using the elimination method?1 solutions Answer 344297 by Maths68(1474)   on 2011-10-17 01:36:54 (Show Source): You can put this solution on YOUR website!0.3x-0.2y=4...............(1) 0.2x + 0.3y=29/19.........(2) Make above equations more simple 3x/10+2y/10=4 Multiply by 10 both sides of above equation 3x+2y=40.................(3) 2x/10+3y/10=29/19 Multiply by 10 both sides of above equation 2x+3y=290/19.............(4) Multiply (3) by -2 and (4) by 3 and add the resultant equations -6x-4y=-80 6x+9y=870/19 ------------------ 5y=870/19-80 5y=(870-1520)/19 5y=-650/19 5y/5=-650/19/5 y=-130/19 Put the value of y in (3) 3x+2y=40.................(3) 3x+2(-130/19)=40 3x-260/19=40 Multiply by 19 both sides 57x-260=760 57x=760+260 57x=1020 57x/57=1020/57 x=1020/57 x, y =1020/57,-130/19 Check Put the values of x and y in (4) 2x+3y=290/19.............(4) 2(1020/57)+3(-130/19)=290/19 2040/57-390/19=290/19 (2040-1170)/57=290/19 870/57=290/19 290/19=290/19
 Rectangles/516171: The length of a rectangle is 5 more than it's width. the perimeter is 9 times more then the width. what are the dimensions of the rectangle1 solutions Answer 344286 by Maths68(1474)   on 2011-10-17 00:15:34 (Show Source): You can put this solution on YOUR website!Length = l=w+5 Width = w=? Perimeter = p = 9w ============================== Perimeter of a Rectangle = length + length + width + width Perimeter of a Rectangle =2 length +2 width P = 2l + 2w 9w=2(w+5)+ 2w 9w=2w+10+2w 9w=4w+10 9w-4w=10 5w=10 5w/5=10/5 w=2 ============================ Dimensions of the Rectangle Length = l=w+5 = 2+5 =7 Width = w=2 Perimeter = p = 9w = 9*2=18
 Linear-equations/516173: 4(2x-3)=-2(3x-8) what is x?1 solutions Answer 344263 by Maths68(1474)   on 2011-10-16 22:22:12 (Show Source): You can put this solution on YOUR website!4(2x-3)=-2(3x-8) 8x-12=-6x+16 8x+6x=16+12 14x=28 14x/14=28/14 x=2 Check 4(2x-3)=-2(3x-8) 4(2(2)-3)=-2(3(2)x-8) 4(4-3)=-2(6-8) 4(1)=-2(-2) 4=4
 Linear-equations/515775: Can you solve these problems by substitution? 1.) x + 2y = -1 4x - 5y = 22 2.) -3x + 7y = 14 2x - y = -131 solutions Answer 344165 by Maths68(1474)   on 2011-10-16 13:32:03 (Show Source): You can put this solution on YOUR website! 1.) x + 2y = -1............(1) 4x - 5y = 22...........(2) Multiply (1) by -4 and add to (2) -4x-8y=4 4x-5y=22 -13y=26 -13y/-13=26/-13 y=-2 Put the value of y in (1) x+2y=-1 x+2(-2)=-1 x-4=-1 x=-1+4 x=3 x,y = 3, -2 Check Put the values of x and y in (1) x + 2y = -1............(1) 3+2(-2)=-1 3-4=-1 -1=-1 2.) -3x + 7y = 14 ..........(1) 2x - y = -13...........(2) Multiply (2) by 7 and add to (2) -3x + 7y = 14 14x - 7y = -91 -------------- 11x=-77 11x/11=-77/11 x=-7 Put the value of x in (2) 2x - y = -13...........(2) 2(-7)-y=-13 -14-y=-13 -y=-13+14 -y=1 y=-1 x,y=-7,-1 Check Put the values of x and y in (2) 2(-7) - (-1) = -13 -14 + 1 = -13 -13=-13
 Rectangles/515791: The length of a rectangle is 2ft longer than its width. If the perimeter of the rectangle is 40ft , find its area. 1 solutions Answer 344163 by Maths68(1474)   on 2011-10-16 13:13:02 (Show Source): You can put this solution on YOUR website!Perimeter = P = 40 ft Width = w Length = w+2 Perimeter = 2l +2w 40=2(w+2)+2w 40=2w+4+2w 40=4w+4 40-4=4w 36=4w 36/4=4w/4 9=w w=9 Perimeter = P = 40 ft Width = w = 9 Length = w+2 = 9+2 = 11
 Linear-equations/515785: Solve this problem through substitution: x + y = 6 x - y = -21 solutions Answer 344161 by Maths68(1474)   on 2011-10-16 13:08:34 (Show Source): You can put this solution on YOUR website!x + y = 6 ...........(1) x - y = -2 ..........(2) Add (1) and (2) x + y = 6 x - y = -2 ------------ 2x=4 2x/2=4/2 x=2 Put the value of x in (1) x + y = 6 ...........(1) 2+y=6 y=6-2 y=4 x,y=2,4
 Age_Word_Problems/515764: A man is 4 times as old as his son. Five years ago, the sum of their ages was 30.Form an equation in a variable of your choice and hence calculate their present ages.1 solutions Answer 344156 by Maths68(1474)   on 2011-10-16 12:43:41 (Show Source): You can put this solution on YOUR website!A man is 4 times as old as his son. Five years ago, the sum of their ages was 30.Form an equation in a variable of your choice and hence calculate their present ages. Let Present age of Man = m Present age of Son = s Man is 4 times as old as his son. m=4s..........(1) Five years ago, m-5=s-5 the sum of their ages was 30 (m-5)+(s-5)=30 m-5+s-5=30 m+s-10=30 m+s=30+10 m+s=40.............(2) Put the value of m from (1) to (2) 4s+s=40 5s=40 5s/5=40/5 s=8 Put the value of s in (1) m=4s m=4(8) m=32 Present age of Man = m = 32 years old Present age of Son = s = 8 years old
 expressions/515766: Can you show me how to solve this problem: 6y-2+2y=141 solutions Answer 344153 by Maths68(1474)   on 2011-10-16 12:38:06 (Show Source): You can put this solution on YOUR website!6y-2+2y=14 8y-2=14 8y=14+2 8y=16 8y/8=16/8 y=2
 Numbers_Word_Problems/515765: when 4 is added to a number and the result is divided by 3, the answer is 5. Find the number.1 solutions Answer 344151 by Maths68(1474)   on 2011-10-16 12:33:56 (Show Source): You can put this solution on YOUR website!Let Number = x (4+x)/3=5 (4+x)=5*3 4+x=15 x=15-4 x=11 Number is 11
 Linear_Algebra/515747: Saidhari bought a toaster oven for 90 dollars. this price was 1/4 off the list price. what was the list price.1 solutions Answer 344150 by Maths68(1474)   on 2011-10-16 12:31:25 (Show Source): You can put this solution on YOUR website!Saidhari bought a toaster oven for 90 dollars. this price was 1/4 off the list price. what was the list price. List price = x 1/4 of list price = x(1/4)=x/4 List pirce - discount = Discounted price x-x/4=90 4x-x/4=90 3x/4=90 x=90*4/3 x=30*4 x=120 List price = \$120
 Linear-systems/515732: solve for r, 36r^2-1=0 1 solutions Answer 344142 by Maths68(1474)   on 2011-10-16 11:35:20 (Show Source): You can put this solution on YOUR website!solve for r, 36r^2-1=0 36r^2-1=0 (6r)^2-(1)^2=0 (6r-1)(6r+1)=0 (6r-1)=0 or(6r+1)=0 6r=1 or6r=-1 r=1/6 or r=-1/6
 Expressions-with-variables/515716: solve for x ax-x=c Here is what I've come up with... x=c/a-1 Is this correct?1 solutions Answer 344140 by Maths68(1474)   on 2011-10-16 11:30:46 (Show Source): You can put this solution on YOUR website!You are right well done! Keep it up!! solve for x ax-x=c x(a-1)=c x(a-1)/(a-1)=c/(a-1) cancel out (a-1) from left hand side of the equation x=c/(a-1)
 Linear_Equations_And_Systems_Word_Problems/515724: sara and jim both decided to save some money each week. sara has already saved 4100, and she plans to save \$10 a week. jim plans to save \$15 a week. in how many weeks will jim and sara have saved the same amount?1 solutions Answer 344138 by Maths68(1474)   on 2011-10-16 11:21:26 (Show Source): You can put this solution on YOUR website! Let it takes x weeks to equalize their savings. 15*x=4100+10*x 15x=4100+10x 15x-10x=4100 5x=4100 5x/5=4100/5 x=820 After 820 weeks or 205 months or 17 years, one month and one week !!!!!
 Expressions-with-variables/515722: Solve the equation for y. Then find the value for y for each value x. 6x=7-4y; x= -2, -1, 01 solutions Answer 344137 by Maths68(1474)   on 2011-10-16 11:09:55 (Show Source): You can put this solution on YOUR website!6x=7-4y 4y=-6x+7 4y/4=(-6x+7)/4 y=(-6x+7)/4 ===================== x=-2 y=(-6(-2)+7)/4 y=(12+7)/4 y=19/4 =================== x=-1 y=(-6(-1)+7)/4 y=(6+7)/4 y=13/4 ================= x=0 y=(-6(0)+7)/4 y=7/4
 Expressions-with-variables/515719: Solve the equation for y. Then find the value for y for each value x. 4x=3y-7; x= a, 5, 61 solutions Answer 344136 by Maths68(1474)   on 2011-10-16 11:02:57 (Show Source): You can put this solution on YOUR website!4x=3y-7; x= a, 5, 6 4x=3y-7 rearrange above equation 3y-7=4x 3y=4x+7 3y/3=(4x+7)/3 y=(4x+7)/3 =========================== Now x=a y=(4a+7)/3 ========================== x=5 y=(4(5)+7)/3 y=(20+7)/3 y=27/3 y=9 ========================== x=6 y=(4(6)+7)/3 y=(24+7)/3 y=24/3+(7/3) y=8+(7/3)
 Age_Word_Problems/515636: two years ago father was 3 times as old as his son and 2 year hence,twice his age will be equal to 5 times that of his son find present age ?1 solutions Answer 344102 by Maths68(1474)   on 2011-10-16 02:39:55 (Show Source): You can put this solution on YOUR website!Let Present age of Father = f Present age of Son = s Two years ago f-2=s-2 Father was 3 times as old as his son f-2=3(s-2) f-2=3s-6 f=3s-6+2 f=3s-4............(1) and 2 year hence, f+2=s+2 then twice his age will be equal to 5 times that of his son 2(f+2)=5(s+2) 2f+4=5s+10 2f=5s+10-4 2f=5s+6.............(2) Put the value of f in (2) from (1) 2(3s-4)=5s+6 6s-8=5s+6 6s-5s=6+8 s=14 Put the value of s in (1) f=3s-4............(1) f=3(14)-4 f=42-4 f=38 Present age of Father = f = 38 years old Present age of Son = s = 14 years old
 Age_Word_Problems/515634: Rico is twice old as Ryan.In four years,Rico's age will be three times as Ryan's age is six years ago.How old are they now?1 solutions Answer 344101 by Maths68(1474)   on 2011-10-16 02:29:14 (Show Source): You can put this solution on YOUR website!Let Present age of Rico = r Present age of Ryan = y Rico is twice old as Ryan r=2y........(1) In four years,Rico's age will be three times as Ryan's age is six years ago Rico age in four years = r+4 Ryan age six years ago = y-6 r+4=3(y-6) r+4=3y-18 r=3y-18-4 r=3y-22.............(2) Put the value of r in (2) from (1) 2y=3y-22 2y-3y=-22 -y=-22 Multiply by -1 both sides y=22 Put the value of y in (1) r=2y r=2(22) r=44 Present age of Rico = r = 44 years old Present age of Ryan = y = 22 years old Six years ago Ryan was = 22-6 = 16 In four years Rico will be = 44+4 = 48 (which is 3 times of 16)
 Age_Word_Problems/513251: In 36 years, Anna will be five times as old as she is today. How old is Anna?1 solutions Answer 344100 by Maths68(1474)   on 2011-10-16 02:17:35 (Show Source): You can put this solution on YOUR website!Let Present age of Anna = a In 36 years a+36=5a a+36=5a a-5a=-36 -4a=-36 -4a/-4=-36/-4 a=9 Anna is 9 years old now. In 36 years she will be =(36+9)= 45 (which is 5 times of 9)
 Age_Word_Problems/513480: selma is now 3 times as old as joyce. four years ago, selma was 4 times as old as joyce was then. find their present ages. 1 solutions Answer 344099 by Maths68(1474)   on 2011-10-16 02:08:10 (Show Source): You can put this solution on YOUR website!Let Present age of Selma = s Present age of Joyce = j selma is now 3 times as old as joyce s=3j........(1) Four years ago, s-4=j-4 then Selma was 4 times as old as joyce s-4=4(j-4) s-4=4j-16 s=4j-16+4 s=4j-12.............(2) Put the value of s in (2) from (1) 3j=4j-12 3j-4j=-12 -j=-12 Multiply by -1 both sides j=12 Put the value of j in (1) s=3j s=3(12) s=36 Present age of Selma = s = 36 years old Present age of Joyce = j = 12 years old
 Age_Word_Problems/513424: In 1985 Maria was three times as old as Sue. Five years earlier, the sum of their ages was eighteen. In what year was Maria born?1 solutions Answer 344098 by Maths68(1474)   on 2011-10-16 02:00:48 (Show Source): You can put this solution on YOUR website! In 1985 ======== Maria was = m years old Sue was = s years old Maria was three times as old as Sue m=3s........(1) 1980 ==== Five years earlier (s-5)+(m-5)=18 s-5+m-5=18 s+m-10=18 s+m=18+10 s+m=28.......(2) ============================================================================= Put the value of m from (1) to (2) s+(3s)=28 s+3s=28 4s=28 4s/4=28/4 s=7 Put the value of s in (1) m=3s m=3(7) m=21 In 1985 Maria was = m = 21 years old Sue was = s = 7 = years old Maira was born in = 1985 - 21 = 1964