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# Recent problems solved by 'mananth'

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 Linear_Algebra/613837: An airplane flying against the wind travels 242 miles in the same time that it can travel 253 miles with the wind. If the wind sped is 15 miles per hour, what is the speed of the airplane in still air ?1 solutions Answer 386309 by mananth(12270)   on 2012-05-22 20:53:46 (Show Source): You can put this solution on YOUR website!Plane speed x mph wind speed 15 mph .. against wind x - 15 mph with wind x + 15 mph Distance against wind 242 Distance with wind 253 Time = same equate the time against with time with current t=d/r 242 /(x- 15 )= 253 /(x+ 15 ) 242 *(x+ 15 )= 253 *(x- 15 ) 242 x + 3630 = 253 x -3795 242 x -253 x = -3795 + -3630 -11 x = -7425 / -11 x= 675 mph m.ananth@hotmail.ca
 Money_Word_Problems/613861: A worker received a \$10,000 bonus and decided to split it among three different accounts. He placed part in a savings account paying 4.5% per year, twice as much in government bonds paying 5%, and the rest in a mutual fund that returned 4%. His income from these investments after one year was \$455. How much did the worker place in each account?1 solutions Answer 386304 by mananth(12270)   on 2012-05-22 20:42:43 (Show Source): You can put this solution on YOUR website!\$ 10,1000 - Total Savings = x------- 4.5% Bonds=2x-------5% (10000-3x)-----4% Interest = 455 4.5%x+5%*(2x)+(10000-3x)*4%= 455 multiply equation by 100 4.5x+10x+40000-12x=45500 2.5x=45500-40000 2.5x=5500 x= 5500/2.5 x= 2200 so you know how much he invested in other accounts
 Equations/612506: The current in a river is 6 miles per hour. In her motorboat Marissa can travel 12 miles upstream or 16 miles downstream in the same amount of time. What is the speed of her motorboat in still water?1 solutions Answer 385615 by mananth(12270)   on 2012-05-19 00:13:47 (Show Source): You can put this solution on YOUR website!Boat speed x mph current speed 6 mph .. against current x - 6 mph with current x + 6 mph Distance against current 12 Distance with current 16 Time = same equate the time against with time with current t=d/r 12 /(x- 6 )= 16 /(x+ 6 ) 12 *(x+ 6 )= 16 *(x- 6 ) 12 x + 72 = 16 x -96 12 x -16 x = -96 + -72 -4 x = -168 / -4 x= 42 mph m.ananth@hotmail.ca
 Travel_Word_Problems/612588: a bridge in a state is 450 feet long. phil and heim started walking across the bridge at the same time. heim's speed was 2 feet per minute faster then phil's. if heim finished walking across the brdige 2.5 minutes before phil, find phil's average speed in feet per minute. Phil's average speed is ___ feet per minute1 solutions Answer 385614 by mananth(12270)   on 2012-05-18 23:56:09 (Show Source): You can put this solution on YOUR website!Let Phil's apeed be x ft/m Heim's speed = x+2 ft/m distance = 450 ft time = distance/speed time taken by Phil - time taken by Heim = 2.5 450/x - 450/(x+2)= 2.5 LCD = x(x+2) multiply equation by LCD 450(x+2)-450x= 2.5x(x+2) 450x+900-450x=2.5x^2+5x 2.5x^2+5x-900=0 /2.5 x^2+2x-440=0 x^2+22x-20x-440=0 x(x+22)-20(x+22)=0 (x+22)(x-20)=0 x= 20 OR -22 speed cannot be negative. so phil's speed = 20ft/m
 Length-and-distance/612594: given A(-2,1)and B(8,5) the end points of the diameter of the circle a) what are the coordinates of the center W of the circle? b) what is the radius of this circle 1 solutions Answer 385613 by mananth(12270)   on 2012-05-18 23:47:53 (Show Source): You can put this solution on YOUR website!The center is the mid point If the coordinates of A and B are ( x1, y1) and ( x2, y2) respectively, then the midpoint, M, of AB is given by the following formula (-2,1)(8,5) M(x,y) = x= (-2+8)/ 2y=(1+ 5 )/ 2 x= 3 ,y= 3 ( 3 , 3 ) Radius is the distance from center to one of the endponts of the diameter . Distance between two points x1 y1 x2 y2 (3 3) (8 5) d= d= d= d= d= 5.39 m.ananth@hotmail.ca
 Geometry_Word_Problems/612598: a dirt path 4 feet width surrounds a rectangular garden that is 38 feet longer and 17 feet wide. find the area of the dirt path?1 solutions Answer 385612 by mananth(12270)   on 2012-05-18 23:39:51 (Show Source): You can put this solution on YOUR website!Length of garden 38 feet Width = 17 feet width of dirtpath= 4 feet Area = 38 * 17 646 ft^2 Length of garden +width of dirtpath 38 + 4 Width of garden + width of dirtpath 17 + 4 Area ofgarden + dirt path=(38+4 )(17+4) Area ofgarden + dirt path=42*21 Area ofgarden + dirt path=882 Area of walkway = area of (pool+walkway)-areaof garden= 882 - 646 Area of dirt Path=236 ft^2
 Linear_Equations_And_Systems_Word_Problems/612605: one number is 2 more than the another number.their sum is 64.what is the number 1 solutions Answer 385611 by mananth(12270)   on 2012-05-18 23:27:30 (Show Source): You can put this solution on YOUR website!let one number be x the other number be y x=y+2 x-y=2---------(1) x+y=64---------(2) add equation (1) & (2) 2x= 66 /2 x=33 y =33-2 y=31 the numbers are 31 & 33
 Geometry_Word_Problems/608827: the height of a triangle is 10 centimeters more than its base. if the area of the triangle is 100 cm, find its base and height 1 solutions Answer 383396 by mananth(12270)   on 2012-05-08 20:39:49 (Show Source): You can put this solution on YOUR website!let base = x cm height = (x+10) cm Area of triangle = 1/2 * base * height 100= 1/2 * x*(x+10) multiply by 2 (x+20)(x-10)=0 x= -20 or 10 Ignore negative base = 10 cm height = 20 cm
 Expressions-with-variables/608828: Please Help Me With My Home Work Question........ I Am Doing Algebraic Expressions.... An I Have To Write An Expression That Matches Each Description An I Am Really Lost So Please Could You Help Me??? 1 solutions Answer 383392 by mananth(12270)   on 2012-05-08 20:35:59 (Show Source): You can put this solution on YOUR website!where is the question?
 Mixture_Word_Problems/608819: You have 2 mixtures of a saline solution that are 12% by volume, and 20% by volume. You need 6 gallons of a solution that is 18% by volume for an experiment. How much of the 12% and the 20% solutions should you mix together?1 solutions Answer 383391 by mananth(12270)   on 2012-05-08 20:35:16 (Show Source): You can put this solution on YOUR website!Solution I --12%---x gal Solution II--20%---(6-x)gal Mixture total ---- 18% -----6 gal 12%*x+(6-x)*20%= 6*18% multiply equation by 100 12x+(6-x)*20 = 108 12x+120-20x=108 12x-20x=108-120 -8x=-12x /-8 x=-12/8 x=3/4 gallons --- 6% solution Balance of 6 gallons is 20% solution 6-3/4 = 5 1/4 gallons
 Pythagorean-theorem/608784: How would you solve x^2 +3^2 = 4x^2? 1 solutions Answer 383389 by mananth(12270)   on 2012-05-08 20:28:42 (Show Source): You can put this solution on YOUR website! add -x^2 to both sides /3 take the square root x=+/- 1
 test/608812: if x-17=25 then x= what?1 solutions Answer 383387 by mananth(12270)   on 2012-05-08 20:25:11 (Show Source): You can put this solution on YOUR website!x-17=25 add 17 to both sides x-17+17 = 25+17 x=42
 Surface-area/608813: A 5 by seven inch rectangular picture has a frame of uniform width.If the outer edge of the frame is to have a perimeter of 32 inches , how wide should the frame be?1 solutions Answer 383385 by mananth(12270)   on 2012-05-08 20:23:52 (Show Source): You can put this solution on YOUR website!length of picture=7 in width of frame = 5in uniform width all round = x inches length of frame = 7+x width = 5+x Perimeter of frame = 2(L+W) =2(7+x+5+x) 2(2x+12)= 32 /2 2x+12=16 -12 2x=4 /2 x=2 width = 2inch wide
 Linear-systems/606993: i am hoping that you can help me with this linear systems by substitution question y=2x-1 x+5y=281 solutions Answer 382333 by mananth(12270)   on 2012-05-03 21:30:58 (Show Source): You can put this solution on YOUR website!1 x + 5 y = 28 .............1 5 y = 28- x / 5 = y = 5.6-0.2 x -2x+y = -1 Substitute y in (2) -2x+1(5.6-0.2x)=-2x+5.6 -0.2x=-1 -2x-0.2x=-6.6 -2.2 x = -6.6 / -2.2 x= 3 Plug the value of x in (1) x+5y=28 1*3+5y= 28 3 + 5 y = 28 5 y = 25 / 5 y= 5 m.ananth@hotmail.ca
 Proportions/606982: Jake spent 3/8 of his money on videotape and 1/2 of what was left on a cassette Tape. he now has \$6.25. How much money did he start with?1 solutions Answer 382332 by mananth(12270)   on 2012-05-03 21:26:11 (Show Source): You can put this solution on YOUR website!Let jake have \$x 3x/8 on video tape Balance left = x-3x/8 =5x/8 He spent (1/2) *(5x/8) on cassette tape =(5x/16) So he had a balance of (5x/8)-(5x/16) =5x/16 6.25 = 6 1/4 = 25/4 5x/16 = 25/4 x= (16*25)/(4*5) x= 20 He had \$20
 Graphs/606988: What is the x-intercept and y-intercept for -5x + 5y = -251 solutions Answer 382330 by mananth(12270)   on 2012-05-03 21:15:05 (Show Source): You can put this solution on YOUR website!-5x+5y=-25 /5 -x+y=-1 Y Intercept, plug x=0 y = -1 X intercept ,plug y=0 x=1
 Problems-with-consecutive-odd-even-integers/606961: Chris says, I am thinking of two positive integers that have a difference of 8 and the sum of their squares is 610." Algebraically determine the integers that Chris is thinking of.1 solutions Answer 382329 by mananth(12270)   on 2012-05-03 21:12:27 (Show Source): You can put this solution on YOUR website!if one integer is x the other will be x-8 x^2+(x-8)^2=610 x^2+x^2-16x+64=610 2x^2-16x=546 /2 x^2-8x=273 x^2-8x-273=0 x^2-21x+13x-273=0 x(x-21)+13(x-21)=0 (x-21)(x+13)=0 x=21 OR -13 The integers are positive so the numbers are 21 & 13
 Mixture_Word_Problems/606984: how many ml of that is 10% alcohol must be added to a 500 ml wine of 5% alcohol to make a wine that is 7.5% alcohol?1 solutions Answer 382327 by mananth(12270)   on 2012-05-03 21:04:59 (Show Source): You can put this solution on YOUR website!-------------- percent ---------------- Amount Wine 5 ---------------- 500 ml Alcohol 10 ---------------- x ml Mixture 7.5 ---------------- 500 + x ml 5*500+10x=7.5(500+x) 2500+10x=3750+7.5x 10x-7.5x=-2500+3750 2.5x=1250 / 2.5 x=500 ml Alcohol m.ananth@hotmail.ca
 Quadratic_Equations/606965: Solve the equation by completing the square. 2x^2-x-2=0 What I've tried 2x^2-x-(1/2)^2=2-(1/2)^2 (2x-(1/2))^2=(9/4) 2x-(1/2)=+/-(3/2) 2x=2 or -1 X=1 or -(1/2) Please show all steps.1 solutions Answer 382326 by mananth(12270)   on 2012-05-03 21:02:09 (Show Source): You can put this solution on YOUR website! /2 Third term = (1/2* coefficient of middle term)^2 (1/2 * -1/2)^2=1/16 take the square root x-(1/4) = +/-sqrt(17/16) x= (1/4) +/-sqrt(17)/4) x= 1.28 OR -0.78
 Miscellaneous_Word_Problems/606516: The Johnson County Carnival costs \$15 plus \$0.50 per ride. The Jefferson County Carnival costs \$10 plus \$1.00 per ride. How many rides should you plan on riding to make the Johnson County Carnival less expensive than the Jefferson County Carnival?1 solutions Answer 382098 by mananth(12270)   on 2012-05-02 21:47:08 (Show Source): You can put this solution on YOUR website!Let r be the number of rides The total cost for r rides = Johnson- C(j)= 15+0.5r Jefferson= C(Je)=10+1r Johnson < Jefferson C(j) 15+0.5r<10+1r add -0.5r 15+0.5r-0.5r<10+1r-0.5r 15<10+0.5r -10 15-10<0.5r 5<0.5r /0.5 10 so r > 10
 test/606526: Terri and Juan earned \$1,150 from a one-year investment of \$15,000. If Terri invested some of the money at 8% interest and Juan invested the rest at 7%, how much did each invest?1 solutions Answer 382096 by mananth(12270)   on 2012-05-02 21:40:14 (Show Source): You can put this solution on YOUR website!Terri 8.00%per annum ------------- Amount invested =x Juan 7.00%per annum ------------ Amount invested = y 15000 Interest----- 1150 Sum of investments x + y= 15000 -------------1 Interest earned on both investments 8.00% x + 7.00% y= 1150 Multiply by 100 8 x + 7 y= 115000.00 --------2 Multiply (1) by -8 we get -8 x -8 y= -120000.00 Add this to (2) 0 x -1 y= -5000 divide by -1 y = 5000 Terri 7.00% \$ 5000 Juan 8.00% \$ 10000 CHECK 5000 --------- 7.00% ------- 350.00 10000 ------------- 8.00% ------- 800.00 Total -------------------- 1150.00 m.ananth@hotmail.ca
 Signed-numbers/606527: 2(n+5)=16 what is the valu of n? 1 solutions Answer 382092 by mananth(12270)   on 2012-05-02 21:35:23 (Show Source): You can put this solution on YOUR website!2(n+5)=16 /2 (n+5)=8 -5 n+5-5 = 8-5 n=3
 Numbers_Word_Problems/606473: Number Sense: "The sum of two numbers is eleven. The sum of the squares of the same two numbers is sixty-one. Find the two numbers"1 solutions Answer 382091 by mananth(12270)   on 2012-05-02 21:34:11 (Show Source): You can put this solution on YOUR website!let the numbers be x & y x+y = 11 x^2+y^2= 61 x=11-y x^2=(11-y)^2 substitute x (11-y)^2+y^2= 61 121-22y+y^2+y^2=61 2y^2-22y+121=61 2y^2-22y+60=0 /2 x^2-11y+30=0 x^2-6y-5y+30=0 x(x-6)-5(x-6)=0 (x-6)(x-5)=0 x= 5 OR 6 so y= 6 OR 5 (5,6) OR (6,5)
 Volume/606503: a fish tank measures 12 inches by 24 inches and has a height of 15 inches.Jaime is filling the tank using a can he found in the kitchen.the last full can of water was added and the water level raised from 10.5 inches to 11 inches. what is the volume of the can? be sure to show your work. 1 solutions Answer 382087 by mananth(12270)   on 2012-05-02 21:21:24 (Show Source): You can put this solution on YOUR website!The area of the tank is 12 * 24 the increase in height by filling one can full of water = 0.5 in so increase in volume = 12*24*0.5 =48 cu.in This is the volume of the can.
 Numbers_Word_Problems/606476: Two consecutive positive odd integers have a sum which is less than 18. Which pair of integers does not solve this problem? 2 and 5 1 and 3 7 and 9 5 and 71 solutions Answer 382086 by mananth(12270)   on 2012-05-02 21:17:37 (Show Source): You can put this solution on YOUR website!2 & 5 ( 2 is even)
 Linear-systems/606505: solve the elmination method -5x+6y=18 15x-18y=201 solutions Answer 382084 by mananth(12270)   on 2012-05-02 21:13:41 (Show Source): You can put this solution on YOUR website!-5 x + 6 y = 18 .............1 15 x -18 y = 20 .............2 Eliminate y multiply (1)by 3 Multiply (2) by 1 -15 x 18 y = 54 15 x -18 y = 20 Add the two equations 0 x = 74 Ther is no solution . The lines are parallel.
 Geometry_Word_Problems/606474: a can has 3tennis balls, the can is just large enough sothat he tenis balls will fit inside with the lid on. the diameter of each tennis ball is 2.5 inches. what is te volume of the empty space inside the can?1 solutions Answer 382081 by mananth(12270)   on 2012-05-02 21:08:35 (Show Source): You can put this solution on YOUR website!Volume of cylinder - volume of three balls = volume of empty space. Cylinder = pi*r^2*h The height of cylinder = 3 times the diameter of the ball. The radius of cylinder = radius of ball = 3.14 * 1.25^2*7.5 =36.8 cu.in Volume of 1 ball = 4/ 3 * pi* *r^3 =4/3 * pi* 1.25^3 =8.18 cu.in 3 balls volume = 8.18 *3 = 24.54 cu.in empty space = 36.8 - 8.18= 27.68 cu.in
 Mixture_Word_Problems/605166: Algebra: How much of a 14% acid solution should be added to 90 oz. of a 47% solution to get one of 29%? 1 solutions Answer 381596 by mananth(12270)   on 2012-04-30 05:06:38 (Show Source): You can put this solution on YOUR website!-------------- percent ---------------- Amount Acid Solution I 47 ---------------- 90 Oz Acid Solution II 14 ---------------- x Oz Mixture 29 ---------------- 90 + x Oz 47*90+14x=29(90 +x) 4230+14 x=2610 +29x 14x-29x =-4230+ 2610 -15x=-1620 /-15 x=108 Oz Acid Solution II m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/605171: Hi I have a question: ((3x-2)/(x+2))-(2/(x-2)) I know that the answer is 3/(x+2) But I don't understand how? Thanks!1 solutions Answer 381595 by mananth(12270)   on 2012-04-30 05:03:11 (Show Source): You can put this solution on YOUR website! LCD = (x+2)(x-2)
 Travel_Word_Problems/605231: aeroplane travels at speed of 800 km/hr and reaches destination in 3 hours.If it starts 20 min late what should be its speed in km/hr so as to reach destination in time?1 solutions Answer 381594 by mananth(12270)   on 2012-04-30 04:50:24 (Show Source): You can put this solution on YOUR website!distance= speed * time 800*3 = 2400 miles 20 minutes = 1/3 hours when late, time taken = 3-1/3 = 8/3 hours Let x be the increase in speed when it is late. Distance = speed * time 2400 = (800+x)*8/3 7200 = 6400+8x 800=8x /8 100 = x The speed increase will be 100 km/h so the speed will be 800+100 = 900 km/h
 Numbers_Word_Problems/605163: Mr. Ang invested Php 16,000, a part of it at 9% and the rest at 4%, his total interest from at both investments was 900. how much he invest at each rate?1 solutions Answer 381593 by mananth(12270)   on 2012-04-30 04:41:55 (Show Source): You can put this solution on YOUR website!Part I 9.00% per annum ---x Part II 4.00% per annum ---y Sum of investments x + 1 y= 16000 -------------1 Interest earned on both investments 9.00% x + 4.00% y= 900 Multiply by 100 9 x + 4 y= 90000.00 --------2 Multiply (1) by -9 we get -9 x -9 y= -144000.00 Add this to (2) 0 x -5 y= -54000 divide by -5 y = 10800 Part I 4.00% \$ 10800 Part II 9.00% \$ 5200 CHECK 10800 --------- 4.00% ------- 432.00 5200 ------------- 9.00% ------- 468.00 Total -------------------- 900.00 m.ananth@hotmail.ca