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# Recent problems solved by 'mananth'

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 Rational-functions/376030: Clark has a boat that can travel at 15 kph in still water. It can go 140km with the current at the same time it takes to travel 35 km against the current. What is the speed of the river? (Show the complete solution involving Rational Equation)1 solutions Answer 267437 by mananth(12270)   on 2010-11-25 04:50:32 (Show Source): You can put this solution on YOUR website!let speed of current be x kph speed in still water = 15 kph .. speed upstream = 15-x speed downstream = 15+x .. distance upstream = 35 km distance downstream = 140 km. .. time upstream = time downstream .. t = d/r 35/(15-x) = 140/( 15+x) cross multiply 35(15+x) =140(15-x) 525+35x=2100-140x 35x+140x=2100-525 175x=1575 /175 x= 1575/175 x = 9kmh ... speed of current ... m.ananth@hotmail.ca
 Quadratic_Equations/376022: what rate of interest would one need in order to double one's investment in 8 years if interest is compounded daily.1 solutions Answer 267419 by mananth(12270)   on 2010-11-25 02:27:47 (Show Source): You can put this solution on YOUR website!Assume Principal = 100=P Amount = 200=A time = 8 years =n continuously -q=compounding term .. Compound Interest formula i = q([A/P]1/nq - 1). i= 365*((200/100)^(1/(8*365))-1) .. i=0.0866 = 8.66 % ... m.ananth@hotmail.ca
 Percentage-and-ratio-word-problems/375955: P=Rs600,T=5years,R=7%per year 1 solutions Answer 267381 by mananth(12270)   on 2010-11-24 20:09:13 (Show Source): You can put this solution on YOUR website!What is to be found out? ... P=Rs600,T=5years,R=7%per year I = 600*0.07*5 I = 210 Interest = Rs. 210 ... m.ananth@hotmail.ca
 Equations/375952: A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1650 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of the two cars that week? 1 solutions Answer 267379 by mananth(12270)   on 2010-11-24 20:06:32 (Show Source): You can put this solution on YOUR website!A family has two cars. The first car has a fuel efficiency of 40 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1650 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of the two cars that week? .. one car 40 miles /gallon other car 30 miles/gallon .. Total miles = 165 gas used = 45 gallons ... let first car drive x miles second car drive y miles .. x/40 + y/30 = 45 (30x+40y)/30*40 = 45 30x+40y = 45*40*30 30x+40y=54,000............................1 x+y = 1650...............................2 multiply (2) by -30 -30x-30y= 1650*-30 -30x-30y=-49,500 add to (1) 10y=4500 /10 y=450 miles average = 30 consumption = 450/30 = 15 gallons x= 1650-450=1200 miles first car 1200/40 = 30 gallons ... m.ananth@hotmail.ca
 Exponential-and-logarithmic-functions/375929: Find the points where y=-2x-2 intersects with parabola y=.5x^21 solutions Answer 267362 by mananth(12270)   on 2010-11-24 19:35:13 (Show Source): You can put this solution on YOUR website!y=-2x-2 intersects with parabola y=.5x^2 ... -2x-2 = 1/2 * x^2 .. multiply by 2 2(-2x-2)=2*x^2/2 -4x-4 = x^2 reorganize x^2+4x+4=0 (x+2)^2=0 square root x+2=0 x=-2. y = -2x-2 plug value of x y=4-2 y=2 Itintersects at (-2,2,)
 Inequalities/375932: 6p<-48 x/-6<-151 solutions Answer 267361 by mananth(12270)   on 2010-11-24 19:27:10 (Show Source): You can put this solution on YOUR website!6p<-48 divide by 6 6p/6 <-48/6 p<-6 x/-6<-15 multiply by -6 -6*x / -6 > -15/-6 x>15/6 x>5/3 ... m.ananth@hotmail.ca
 Human-and-algebraic-language/375931: If it takes 1 man 4 hrs. to paint a house, and takes another man 6 hrs. to paint the same house, how long would it take for both men working together to paint the house?1 solutions Answer 267358 by mananth(12270)   on 2010-11-24 19:23:59 (Show Source): You can put this solution on YOUR website!one man 4 hours so he does 1/4 of the job in 1 hour. .. other man 6 hours so he does 1/6 of the job in 1 hour ... together 1/4 +1/6 of the job in 1 hour =10/24 =5/12 of the job in 1 day .. they take 12/5 hours= 2.4 hours to paint the house ... m.ananth@hotmail.ca
 Quadratic_Equations/375940: Hi, the problem i am having is with subsitution in a qudratic equation. x^2-xy=10 (1) x+y=8 (2) Thank you. I worked it out using the qudratic formula but i would like to know if it's right before handing my assignment in to my teacher I need it by tommrrow morning please help.1 solutions Answer 267354 by mananth(12270)   on 2010-11-24 19:18:37 (Show Source): You can put this solution on YOUR website!x^2-xy=10 (1) x+y=8 (2) x=8-y plug value of x in (1) (8-y)^2-(8-y)y-10=0 64-16y+y^2-8y+y^2-10=0 2y^2-24y+54=0 /2 y^2-12y+27=0 y^2-9y-3y+27=0 y(y-9)-3(y-9)=0 (y-3)(y-9)=0 y = 3 , y=9 y=3, x=5 y=9,x=-1 ... m.ananth@hotmail.ca
 Word_Problems_With_Coins/375761: please help!! You go to the bank and get change for \$100 in \$1 bills and \$10 bills and there are 55 bills total. How many \$1 bills and how many \$10 bills. 1 solutions Answer 267221 by mananth(12270)   on 2010-11-24 09:12:38 (Show Source): You can put this solution on YOUR website!let \$1 bill be x \$10 bill will be 55-x .. 1*x+10(55-x)=100 x+550-10x=100 -9x+550=100 -550 -550 -9x=100-550 -9x=-450 /-9 x=-450/-9 x= 50 .... \$1 bills y = 5 \$10 bills ... m.ananth@ hotmail.ca ... you can also solve by a linear system x+y =55 x+10y=100 ... multiply first equation by -1 -x-y=-55 add it to second equation 9y = 45 /9 y =5 ... \$10 bills x = \$1 bills ...
 Money_Word_Problems/375746: A firm can sell at a price of \$100 per unit all of a particular commodity it produces. If x units are produced each day, the number of dollars in the total cost of each day's production is x^2+20x+700. How many units should be produced each day so that the firm is guaranteed a profit?1 solutions Answer 267200 by mananth(12270)   on 2010-11-24 08:00:07 (Show Source): You can put this solution on YOUR website!Cost of production of x units = x^2+20x+700. sales from 100 units = 100x .. BREAK EVEN when both are same x^2+20x+700= 100x x^2-80x+700=0 x^2-70x-10x+700=0 x(x-70)-10(x-70)=0 (x-70)(x-10)=0 x= 10 OR 70 .. More than 10 units & less than 70 units must be manufactured to make a profit .... m.ananth@hotmail.ca
 Travel_Word_Problems/375743: A jeepney moves along a straight road at an average speed of 10 meter per second.What is the distance traveled by the jeepney in 2.5 hour?1 solutions Answer 267199 by mananth(12270)   on 2010-11-24 07:45:27 (Show Source): You can put this solution on YOUR website!2.5 hours = 3600 * 2.5 = 9000 seconds ... speed = 10m/s time = 9000 seconds d = rt d=10*9000 = 90,000 meters = 90 km ... m.ananth@hotmail.ca
 Age_Word_Problems/375744: mother's age is 2 more than 5 times the age of her daughter now. two years ago, she was 7 times as old as her daughter. how old are they now?1 solutions Answer 267198 by mananth(12270)   on 2010-11-24 07:38:34 (Show Source): You can put this solution on YOUR website!let daughter's age = x now mother's age = 5x+2 .. Agea 2 years ago daughter = x-2 mother = 5x+2-2=5x ... 5x=7(x-2) 5x=7x-14 -5x 0=2x-14 +14 2x=14 /2 x=7 daughter's age now mother's age = 5x+2 = 5*7 +2= 37 ... m.ananth@hotmail.ca
 Age_Word_Problems/375745: John is 3 years older than Sam. The product of their ages is 54. Find their ages1 solutions Answer 267197 by mananth(12270)   on 2010-11-24 07:33:52 (Show Source): You can put this solution on YOUR website!Sam = x John = x+3 ... x(x+3)=54 x^2+3x=54 x^2+3x-54=0 x^2+9x-6x-54=0 x(x+9)-6(x+9)=0 (x-6)(x+9)=0 x= 6 OR x =-9 (6 & 9) OR (-9, -6) ,, m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/375733: 15^3 * 15^2=1 solutions Answer 267196 by mananth(12270)   on 2010-11-24 07:29:23 (Show Source): You can put this solution on YOUR website!15^3 * 15^2= .. (15)^5 =(3*5)^5 =3^5*5^5 ...
 Rectangles/375738: the length of a retangle is 3 less than 5 times of its width. write a simplified algebraic expression for the perimeter of a rectangle. if the rectangle width is tripled and its length is doubled the perimeter of new rectangle is 92 cm greater than original perimeter. Find the area of the original rectangle.1 solutions Answer 267195 by mananth(12270)   on 2010-11-24 07:05:01 (Show Source): You can put this solution on YOUR website!let width =x length = 5x-3 .. Perimeter = 2(x+5x-3) Perimeter = 2(6x-3) =12x-6 ... new rectangle width = 3x length = 2(5x-3) perimeter = 2(3x+2(5x-3)) perimeter = 2(3x+10x-6) perimeter = 6x+20x-12 ... 6x+20x-12=12x-6+92 6x+20x-12x=-6+92+12 14x=98 /14 x=98/14 x=7 cm. the width of original rectangle length = 5x-3 = 5*7-3 = 32cm ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/375722: Use scientific notation to multiply the following two numbers. Express the answer using scientific notation; retain all nonzero decimal places. (2.6 · 10^2) · (7.3 · 10^3) 1 solutions Answer 267174 by mananth(12270)   on 2010-11-24 05:04:59 (Show Source): You can put this solution on YOUR website!(2.6 · 10^2) · (7.3 · 10^3) = (2.6*7.2*10^2*10^3) =(18.72*10^5) =1.872*10^6 ... m.ananth@hotmail.ca
 Equations/375720: find three consecutive integers whose sum is -1471 solutions Answer 267170 by mananth(12270)   on 2010-11-24 04:40:34 (Show Source): You can put this solution on YOUR website!let the inetegers be x, x+1,x+2 ... x+x+1+x+2=-147 3x+3=-147 -3 -3 3x=-147-3 3x=-150 /3 x= -150/3 x= -50 .. -50,-49,-48 ... m.ananth@hotmail.ca
 test/375596: Hat size 6 7/8 head circumference 21 3/5 head circumference 55. Use ratio and proportion to complete the following 6 7/8 21 3/5 55 7 3/41 solutions Answer 267169 by mananth(12270)   on 2010-11-24 01:21:00 (Show Source): You can put this solution on YOUR website!Hat size 6 7/8 head circumference 21 3/5 head circumference 55. hat size = x ... 6 7/8 = 55/8 21 3/5 = 108/5 ... ... ... multiply by 55 x=17 1/2 ... m.ananth@hotmail.ca
 Travel_Word_Problems/375577: A scout troop hiked 3 miles up a mountain trail. They then hiked back down the same trail. They hiked 2 miles per hour faster coming downhill. the total time for the 6 mile hike was 4 hours. Solve for the rate the troop hiked uphill. 1 solutions Answer 267167 by mananth(12270)   on 2010-11-24 01:07:24 (Show Source): You can put this solution on YOUR website!let them hike uphill at x mph downhill they hike x+2 mph ... distance = 3 miles .. time up + time down = 4 hours ... t = d/r LCD = x(x+2) multiply the equation by x(x+2) .. 3(x+2)+3x=4x^2+8x 3x+6+3x=4x^2+8x reorganize 4x^2+2x-6=0 /2 2x^2+x-3=0 2x^2+3x-2x-3=0 x(2x+3)-1(2x+3)=0 (x-1)(2x+3)=0 x=1 OR x=-3/2 ignore negative uphill rate = 1 mph ... m.ananth@hotmail.ca
 expressions/375648: Solve using the addition principle. a – 3 = 1 1 solutions Answer 267165 by mananth(12270)   on 2010-11-24 00:42:45 (Show Source): You can put this solution on YOUR website!a-3=1 +3 +3 a-3+3=1+3 a=4
 Rectangles/375671: Solve using the multiplication principle first. Then use the elimination method. 2x+y=13 4x + 2y = 23 1 solutions Answer 267164 by mananth(12270)   on 2010-11-24 00:41:09 (Show Source): You can put this solution on YOUR website!2x+y=13 4x + 2y = 23 ... multiply first equation by -2 we have -4x-2y=-26 add this to the second equation 4x-4x+2y-2y = 23-26 0 = -3 ... there is no solution to this system. The lines are parallel. .. ... m.ananth@hotmail.ca
 Linear-equations/375682: Find the missing coordinate of the line that passes through the given points and has the given slope. (x,9)and(4,5) m=2 (9,-4)and(3,y) m=2/31 solutions Answer 267163 by mananth(12270)   on 2010-11-24 00:32:11 (Show Source): You can put this solution on YOUR website!(x,9)and(4,5) m=2 .. slope m = y2-y1/x2-x1 where (x1,y1)& (x2,y2) are the points m= 5-9 / 4-x 2= -4/(4-x) multiply by (4-x) 2(4-x)=-4 8-2x=-4 -8 -2x=-8-4 -2x=-12 /-2 x=6 .. similarly you can work on the next problem. you will walk through m.ananth@hotmail.ca (9,-4)and(3,y) m=2/3
 Rectangles/375681: a rectangular solid has a width that is 2 units shorter than the height. the length is twice the height. let h represent the height. what is an expression for the volume of the rectangular solid?1 solutions Answer 267158 by mananth(12270)   on 2010-11-24 00:09:50 (Show Source): You can put this solution on YOUR website!let height be h length = 2h width = h-2 ... Volume V = L*w*h V= 2h*(h-2)*h V= 2h^2(h-2) V=2h^3-4h^2 ... m.ananth@hotmail.ca
 Mixture_Word_Problems/375680: the sum of the areas of two circles is 612pi square meters. Find the length of a radius of the smaller circle if one of them is 4 times as long as the other.1 solutions Answer 267156 by mananth(12270)   on 2010-11-24 00:06:14 (Show Source): You can put this solution on YOUR website!let the smaller circle radius be r m larger circle radius = 4r m ... area of smaller circle +area of larger circle = 612 pi pi*r^2 + pi*(4r)^2= 612*pi pi(r^2+16r^2)=612*pi /pi 17r^2= 612 /17 r^2= 612/17 r^2= 36 r=6 m the radius of smaller circle. ... m.ananth@hotmail.ca
 Evaluation_Word_Problems/375683: If 4 apples and 2 oranges equals \$1 and 2 apples and 3 oranges equals \$070, how much does each apple and each orange cost?1 solutions Answer 267155 by mananth(12270)   on 2010-11-24 00:01:04 (Show Source): You can put this solution on YOUR website!let each apple cost x each orange cost y .. 4x+2y=1...................1 2x+3y = 0.70..............2 .. multiply (2) by -2 -4x-6y=-1.40 add this to (1) 4x-4x+2y-6y=1-1.40 -4y=-0.4 /-4 y=-0.4/-4 y=0.1 = 10 cents cost of orange plug value of y in (1) 4x+2y=1 4x+2*0.1=1 4x+0.2=1 -0.2 4x=1-0.2 4x=0.8 /4 x=0.8/4 x=0.2= 20 cents = cost of apple ... m.ananth@hotmail.ca
 Evaluation_Word_Problems/375685: If 4 apples and 2 oranges equals \$1 and 2 apples and 3 oranges equals \$070, how much does each apple and each orange cost? show your equation.1 solutions Answer 267154 by mananth(12270)   on 2010-11-23 23:58:29 (Show Source): You can put this solution on YOUR website!let each apple cost x each orange cost y .. 4x+2y=1...................1 2x+3y = 0.70..............2 .. multiply (2) by -2 -4x-6y=-1.40 add this to (1) 4x-4x+2y-6y=1-1.40 -4y=-0.4 /-4 y=-0.4/-4 y=0.1 = 10 cents cost of orange plug value of y in (1) 4x+2y=1 4x+2*0.1=1 4x+0.2=1 -0.2 4x=1-0.2 4x=0.8 /4 x=0.8/4 x=0.2= 20 cents = cost of apple ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/375572: Word Problem help!! A student makes a \$9.75 purchase at the book store with a \$20 bill. The store has no bills and gives the change in quarters and fifty-cent pieces. There are 30 coins in all. How many of each kind are there? How many quarter are there in the change____?1 solutions Answer 267139 by mananth(12270)   on 2010-11-23 22:11:24 (Show Source): You can put this solution on YOUR website!purchase = \$9.75 amount given = \$20 balance to return = \$10.25 ... let quarters be x fifty cent will be the balance = 30-x ... 25x+50(30-x)=1025 cents 25x+1500-50x=1025 -25x+1500 =1025 -1500 -25x=1025-1500 -25x=-475 /-25 x=19 quarters 50 cent pieces will be 30-19=11 ... Check 11*50+19*25= 10.25 = \$10.25 ... m.ananth@hotmail.ca
 Travel_Word_Problems/375650: a train travels 30 mph faster than a caar. if the train covers 120 miles in the same time the car covers 80 miles, what is the speed of each vehicle1 solutions Answer 267138 by mananth(12270)   on 2010-11-23 22:06:12 (Show Source): You can put this solution on YOUR website!SPEED OF CAR BE X MPH TRAIN = X+30 MPH.. ... train distance = 120 miles car distance = 80 miles .. \.. train time = car time multiply the equation by x*(x+30) .. ... 120x= 80(x+30) 120x=80x+2400 -80x 120x-80x=2400 40x=2400 /40 x= 2400/40 x= 60 mph speed of car speed of train = x+30 = 60+30 = 90 mph ... m.ananth@hotmail.ca
 Graphs/375654: find the solution of the system x+y=8 and y=2x+-1 by accurately graphing both lines and determining their point of the intersection1 solutions Answer 267132 by mananth(12270)   on 2010-11-23 21:51:16 (Show Source): You can put this solution on YOUR website!x+y=8 (RED LINE) ... x=0 , y=8 x=1, y =7 x=-1, y=9 x=-2, y=10 .... y=2x+-1 (GREEN LINE ) y=2x-1 x=0, y=-1 x=1,y=1 x=-1y=-3 x=-2, y=-5 ... Plot the points on the graph ... .. locate the point of intersection and find the coordinates They intersect at (3,5) ... m.ananth@hotmail.ca
 Travel_Word_Problems/375661: the store is 60 miles away how long will it take me to get there driving 40 mph the whole time.1 solutions Answer 267130 by mananth(12270)   on 2010-11-23 21:38:50 (Show Source): You can put this solution on YOUR website! distance = 60 miles rate = 40 mph hours = 1 1/2 hours ... m.ananth@hotmail.ca
 Geometry_Word_Problems/375655: The length of a rectangle is 15 cm more than its width. A second rectangle whose perimeter is 72 cm is 5 cm wider but 2 cm shorter than the first rectangle. What are the dimensions of each rectangle?1 solutions Answer 267129 by mananth(12270)   on 2010-11-23 21:36:20 (Show Source): You can put this solution on YOUR website!FIRST RECTANGLE let x be the width length = x+15 ... SECOND RECTANGLE 5 cm wider = x+5 2cm shorter = x+15-2=x+13 .. 2*(l+w)=perimeter 2*((x+5)+(x+13))=72 2*(x+5+x+13)=72 2*(2x+18)=72 divide by 2 2x+18= 72/2 2x+18=36 -18 -18 2x+18=18=36-18 2x=18 /2 x=18/2 x=9 the width length = x+15 = 9+15=24 FIRST RECTANGLE WIDTH 9 CM LENGTH = 24 SECOND RECTANGLE WIDTH = x+5 = 9+5=14 LENGTH = x+13= 9+13=22 ... CHECK 2*14+2*22=72 ... m.ananth@hotmail.ca