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# Recent problems solved by 'mananth'

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 Mixture_Word_Problems/441789: Martin needs to mix some 40% alcohol solution with some 90% alcohol solution to obtain 15 liters of an 80% solution. How much of the 40% solution and how much of the 90% solution should he use? I need the answer quickly, so it would be greatly appreciated if I could receive an answer within a few hours. Thank you very much.1 solutions Answer 304822 by mananth(12270)   on 2011-04-28 03:31:34 (Show Source): You can put this solution on YOUR website! percent ----------------quantity Alcohol 40 ----------------x Alcohol 90 ----------------15-x Total 80.00% ----------------15 40x+90(15-x)=80 *15 40x+1350-90x=1200 40x-90x =1200-1350 -50x=-150 /-50 x=3 liters 40.00% 12 liters 90.00%
 Travel_Word_Problems/441791: Anna & John both travel to their new home 400 miles away. Anna drive at avrg speed of 60mph. where as John at 50mph. during journey Anna stops over for 1h.20 min and john stops half as long .what is the difference in minutes between their arrival time ??1 solutions Answer 304820 by mananth(12270)   on 2011-04-28 03:26:08 (Show Source): You can put this solution on YOUR website!Anna speed = 60 mph so she will take 400/60 =6 hours 40 minutes without a halt She halts for 1hour 20 hours So she takes 8 hours ... John speed = 50 mph. So he takes 400/50 = 8 hours without halt. he halts for 40 minutes so he takes 8 hours 40 minutes to reach difference 40 minutes
 Numbers_Word_Problems/441732: The sum of two numbers is 25 their difference is 9 what are the two numbers?1 solutions Answer 304819 by mananth(12270)   on 2011-04-28 03:19:20 (Show Source): You can put this solution on YOUR website!Let x & y be the numbers x+y=25 x-y=9 add the two equations 2x=34 /2 x=17 17 & 8 are the numbers
 Miscellaneous_Word_Problems/441209: Bayside insurance offers two health plans. Under plan A, Giselle would have to pay the first \$160 of her medical bills, plus 25% of the rest. Under plan B, Giselle would pay the first \$240, but only 20% of the rest, for what amount of medial bills will plan B save Giselle money? Assume she has over \$240 in bills1 solutions Answer 304577 by mananth(12270)   on 2011-04-27 09:08:30 (Show Source): You can put this solution on YOUR website!let the bill amount be x Plan A= 160 + 25.00% of rest Plan B= 240 + 20.00% of the rest Plan B < Plan A 240+0.25(x-240)<160+0.25(x-160 ) 240+0.20x-60<160+0.25x-40 240-160 -60+40 <0.25x-0.2x 60<0.05 x 1200 < x X > 1200 for plan B to save money
 Numbers_Word_Problems/441228: The sum of two numbers is 50. Two times the first number is ten more than the second. Find the two numbers.1 solutions Answer 304576 by mananth(12270)   on 2011-04-27 09:02:34 (Show Source): You can put this solution on YOUR website!let one number be x & the other y 1 x + 1 y = 50 .............1 2 x + -1 y = 10 .............2 Add the two equations 3 x = 60 / 3 x = 20 plug value of x in (1) 1 x + 1 y = 50 20 + 1 y = 50 1 y = 50 -20 1 y = 30 y = 30
 Graphs/440722: Could someone please help me to graph the line containing the given pair of points and find the slope? (6, 3) (-5, -2)1 solutions Answer 304358 by mananth(12270)   on 2011-04-26 09:14:21 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 6 3 -5 -2 slope m = (y2-y1)/(x2-x1) 0.45 m= 0.45 Plug value of the slope and point (6,3)in Y =mx+b 3.00=2.73+b b=3-2.73 b=0.27 So the equation will be Y =0.45x+0.27
 Evaluation_Word_Problems/440728: Hello, I need help on two problems using the substitution method; The solution to the system of equation below is (8,4) 3x-5y 7x + 3y = 68 The second problem is: Bill invested some money at 5% annual interest, and Jeanette invested some at 7%. If their combined interest was \$310 on a total investment of \$5,000, how much did Bill invest? Thanks in advance1 solutions Answer 304355 by mananth(12270)   on 2011-04-26 09:05:38 (Show Source): You can put this solution on YOUR website!Bill 5.00% per annum Jeanette 7.00% per annum x+y=5000 ------------------------1 5.00%x+7.00%y=\$310.00 Multiply by 100 5x+7y=\$31,000.00 --------2 Multiply (1) by -5 we get -5x-5y= -25000.00 Add this to (2) 2y=\$6,000.00 divide by 2 y= \$3,000.00 investment at 7.00%---- Jeanette Balance \$2,000.00 investment at 5.00% --- Bill
 Linear-equations/440662: Could you please put these two equations in slope-intercept form? -3x+y=-12 -6x+2y=-24 Thank You!1 solutions Answer 304337 by mananth(12270)   on 2011-04-26 02:20:44 (Show Source): You can put this solution on YOUR website!-3x+y=-12 y=3x-12 -6x+2y=-24 2y=6x-24 /2 y=3x-12
 Travel_Word_Problems/440674: two cars leave an intersection. One car travela north the other east. When the car traveling north had gone 9 mi, the distance between the cars was 3 mi more than the distance traveled by the car heading east. How far had the eastbond car travled?1 solutions Answer 304336 by mananth(12270)   on 2011-04-26 02:17:47 (Show Source): You can put this solution on YOUR website!let east bound car travel x miles North bound - 9 miles At right angles Use pythagoras theorem x^2++9^2=(x+3)^2 x^2+81=x^2+6x+9 6x=72 x=12
 Systems-of-equations/440671: Solve the system of equations. -3x -4y =9 9x +10y =-31 solutions Answer 304335 by mananth(12270)   on 2011-04-26 02:12:37 (Show Source): You can put this solution on YOUR website!-3x-4y=9 .............1 9x+10y=-3 .............2 Eliminate y multiply (1)by 10 Multiply (2) by 4 -30x-40 y=90 36x+40y=-12 Add the two equations 6x=78 /6 x=13 plug value of x in (1) -3x-4y=9 -39-4y=9 -4y=9+39 -4y=48 y=-12
 Linear_Algebra/440651: Solve this: x-3y=8,4x+y=6 by substitution thank you1 solutions Answer 304331 by mananth(12270)   on 2011-04-25 23:40:30 (Show Source): You can put this solution on YOUR website!x-3y=8 .............1 y=6-4x ---------2 y=6-4x Plug the value of y in (1) x-3(6-4x)=8 x-18+12 x= 8 x+12x=8+18 13x=26 /13 x=2 Plug the value of x in (1) x -3y=8 1*2-3y=8 2-3y=8 -3y=6 /-3 y=-2
 Linear_Algebra/440647: pls.solve it! 4x-3y=-4,10x+y=7 Thank you!!! nove_1990@yahoo.com 1 solutions Answer 304329 by mananth(12270)   on 2011-04-25 23:35:06 (Show Source): You can put this solution on YOUR website!4x-3y=-4 .............1 10x+y=7 .............2 Eliminate y multiply (1)by 1 Multiply (2) by 3 4x-3y= -4 30x+3y= 21 Add the two equations 34x= 17 /34 x=0.50 plug value of x in (1) 4x-3y=-4 2-3y=-4 -3y=-4-2 -3y=-6 y=2
 Matrices-and-determiminant/439710: Kate borrows \$10,000. Some is from her friend at 8% annual interest, twice as much as that from her bank at 9%, and the remainder from her insurance company at 5%. She pays a total of \$830 in interest for the first year. How much did she borrow from each source?1 solutions Answer 303899 by mananth(12270)   on 2011-04-24 05:58:19 (Show Source): You can put this solution on YOUR website!friend ----------- x-------------8% Bank--------------2x-------------9% Insurance company---10,000-3x----5% 8x+9*2x+5(10000-3x)=830*100 8x+18x+50000-15x=83000 11x=83000-50000 11x=33000 /11 x==3000 from friend Bank ---2x= 6000 insurance = 1000
 Miscellaneous_Word_Problems/439716: the sum of two numbers is twenty five. twice the larger number is equal to three times the smaller one. find the two numbers. 1 solutions Answer 303896 by mananth(12270)   on 2011-04-24 05:42:21 (Show Source): You can put this solution on YOUR website!x+y=25...................1 2x=3y 2x-3y=0..................2 Eliminate y multiply (1)by 3 Multiply (2) by 1 3 x + 3 y = 75 2 x + -3 y = 0 Add the two equations 5 x = 75 / 5 x = 15 plug value of x in (1) 1 x + 1 y = 25 15 + 1 y = 25 1 y = 25-15 1 y = 10
 Miscellaneous_Word_Problems/439717: one apple and five oranges cost twenty nine rupees while three apples and four oranges cost thirty two rupees. find the total cost of four apples and five oranges.1 solutions Answer 303895 by mananth(12270)   on 2011-04-24 05:38:55 (Show Source): You can put this solution on YOUR website!Apple ----------x Orenge ------------ y 1 x + 5 y = 29 .............1 3 x + 4 y = 32 .............2 Eliminate y multiply (1)by -4 Multiply (2) by 5 -4 x -20 y = -116 15 x 20 y = 160 Add the two equations 11 x = 44 / 11 x = Rs 4.00 Apple plug value of x in (1) 1 x + 5 y = 29 4 + 5 y = 29 5 y = 29 -4 5 y = 25 y = Rs 5.00 Orange
 Mixture_Word_Problems/439343: What quantity of 80 per cent acid solution must be mixed with a 30 per cent solution to produce 1050 mL of a 50 per cent solution? mL of acid solution = 1 solutions Answer 303682 by mananth(12270)   on 2011-04-22 23:47:29 (Show Source): You can put this solution on YOUR website! percent ---------------- quantity Acid I 80 ---------------- x Acid II 30 ---------------- 1050 - x Total 50.00% ---------------- 1050 80x+30(1050-x)= 50*1050 80x+31500-30x=52500 80x-30x =52500-31500 50x=21000 /50 x=420 ml 80.00% 630 ml 30.00%
 Finance/439388: Bayside insurance offers two health plans. Under plan a, Giselle would have to pay the first \$70 of her medical bills, plus 35% of the rest. Under plan b, Giselle would have to pay the first \$230 and 30% for of the rest. For what amount of medical bills will plan b save Giselle money?1 solutions Answer 303679 by mananth(12270)   on 2011-04-22 23:41:20 (Show Source): You can put this solution on YOUR website!let the bill amount be x Plan A= 75 + 35.00% of rest Plan B= 230 + 30.00% of the rest Plan B < Plan A 230+0.35(x-230)<75+0.35*x 230+0.30x-80.5<75+0.35x-26.25 230-75-80.5+26.25<0.35x-0.3x 100.75<0.05x 2015 the bill should be greater than \$2015
 Linear_Equations_And_Systems_Word_Problems/439419: A swimming pool holds 540,000 liters of water. THe pool has two drainage pipes. When the pool is completely full, the first pipe alone can empty it in 180 min, and the second pipe alone can empty it in 120 min. When both pipes are draining together, how long does it take them to empty the pool?1 solutions Answer 303674 by mananth(12270)   on 2011-04-22 23:18:54 (Show Source): You can put this solution on YOUR website!Pipe A 3 hours It does 1/ 3 of the job in 1 hour Pipe B 2 hours It does 1/ 2 of thejob in 1 hour Together they will do 1/ 3 + 1/ 2 Together they will do 5/ 6 of the job in one hour So they will take 1 1/5 hours So they will take 1.2 hours = 72 minutes
 Money_Word_Problems/437643: A woman earns \$900 in interest from two accounts in a year. If she has three times as much invested at 8% as she does at 6%, how much does she have in each account? 1 solutions Answer 302784 by mananth(12270)   on 2011-04-19 02:16:46 (Show Source): You can put this solution on YOUR website!Part I 6.00% per annum -------------x Part II 8.00% per annum ------------y=3x total investment Interest----- \$900.00 6.00% x + 8.00% * 3 x = \$900.00 0.06 x + 0.08 * 3 x = \$900.00 0.06 x + 0.24 x = \$900.00 0.3 x = \$900.00 / 0.3 x= \$3,000.00 --- Part I 3x=\$9,000.00 Part II
 Word_Problems_With_Coins/437670: The bill for 5 glasses of apple juice and 4 salads is \$9.50,but the bill for 4 glasses of apple juice and 5 salads is \$ 10.30. What would be the bill for a glass of juice and a salad?1 solutions Answer 302782 by mananth(12270)   on 2011-04-19 02:10:57 (Show Source): You can put this solution on YOUR website!Apple juice cost x Salad cost ------------ y 5x+4y=9.5 .............1 4x+5y=10.3 .............2 Eliminate y multiply (1)by -5 Multiply (2) by 4 -25x-20 y=-47.5 16x+20y =41.2 Add the two equations -9x=-6.3 /-9 x=0.70 plug value of x in (1) 5x+4y=9.5 3.5+4y=9.5 4y=9.5-3.5 4y=6 y=1.50
 Linear-equations/437699: solve for subsitution 15x-10y=1 15y=2+5x 8x+5y+14 x=52-9y solve equation by graphong x+y=4 y-x=4 solve by elimination 8x-y=47 x+y=161 solutions Answer 302781 by mananth(12270)   on 2011-04-19 02:02:40 (Show Source): You can put this solution on YOUR website!15x-10y=1.............1 15y=2+5x ---------2 /15 y=0.13+ 0.33x Plug the value of y in (1) 15x-10(0.13+0.33x)=1 15x-1.33-3.33x=1 15x-3.33x=1+1.33 11.67x=2.33 /11.67 x=0.2 Plug the value of x in (1) 15x-10y =1 15*0.2-10y=1 3-10y=1 -10y=-2 /-10 y=0.2 ....................... 8x+5y=14 .............1 9y=52-x ---------2 /9 y=5.78-0.11x Plug the value of y in (1) 8x+5(5.78-0.11x)=14 8x+28.89-0.56x=14 8x-0.56x=14-28.89 7.44x=-14.89 /7.44 x=-2 Plug the value of x in (1) 8x+5y=14 8*-2+5y=14 -16+5y=14 5y=30 /5 y=6 .................................. x+y=4 .............1 -x+y =4 .............2 Eliminate y multiply (1)by -1 Multiply (2) by 1 -x-y=-4 -x+y=4 Add the two equations -2x = 0 x=0 plug value of x in (1) x+y=4 y=4 equation1 when x= 0 y=4(0,4) when y =0,x=4(4,0) Equation 2 when x= 0,y=4(0,4) when y =0x=-4(-4,0) ... ................ 8 x + -1 y = 47 .............1 1 x + 1 y = 16 .............2 Eliminate y multiply (1)by 1 Multiply (2) by 1 8 x -1 y = 47 1 x 1 y = 16 Add the two equations 9 x = 63 / 9 x = 7 plug value of x in (1) 8 x + -1 y = 47 56 + -1 y = 47 -1 y = 47 -56 -1 y = -9 y = 9
 Age_Word_Problems/437671: Cory's age is 20% of her father's age. Forty-two years from now, Cory's age will be two-thirds (2/3) of her father's age. How old are Cory and her father now?1 solutions Answer 302773 by mananth(12270)   on 2011-04-18 23:47:20 (Show Source): You can put this solution on YOUR website!cory's age = 20% of father's age so father is 5 times cory's age let cory's age = x father's age = 5x 42 years later Cory's age x+42 father's age 5x+42 If Cory 's age = 2/3 of father's age then father is 1.5 times cory's age father's age 1.5 times older 5x+42=1.5(x+42) 5x+42=1.5x+63 3.5x=63 -42 3.5x=21 /3.5 x=6 Cory's age x+20=26 years father's age
 Triangles/437674: In a right triangle, if one acute angle has measure 6x-10 and the other has measure 2x-4 , find the larger of these two angles1 solutions Answer 302772 by mananth(12270)   on 2011-04-18 23:39:28 (Show Source): You can put this solution on YOUR website!6x-10 and the other has measure 2x-4 6x-10+2x-4=90 8x-14=90 8x=104 /8 x=13 .. 6x-10= 68 2x-4==22 68+22=90
 Travel_Word_Problems/437560: Sarah hikes at 4 kilometers per hour from one end of a trail that is 34 km long. Amanda begins 1 hr laater at the other end. Walks toward sarah at 6 k/m. How long will it take for them to pass each other1 solutions Answer 302737 by mananth(12270)   on 2011-04-18 21:17:06 (Show Source): You can put this solution on YOUR website!Sarah 4 km/h Amanda 6 km/h 1 hours late Distance 37 km 1hour Sarah has traveled 4 km before Amanda starts So distance = 33 When amanda starts Let time they take to meet be x hours Sarah distance traveled 4 x miles Amanda distance traveled 6 x miles Time taken to meet is same t=d/r combined speed= 10 km/h 10 x = 33 2.44 x= 3.3 hours after Amanda starts
 Miscellaneous_Word_Problems/437600: how many gallons of a 50% antifreeze solution must be mixed with 60 gallons of 20% antifreeze to get a mixture that is 40% antifreeze 1 solutions Answer 302726 by mananth(12270)   on 2011-04-18 20:59:31 (Show Source): You can put this solution on YOUR website!------ Percent ---------------- quantity Antifreeze 20 ---------------- 60 Antifreeze 50 ---------------- x Total 40 ---------------- 60 + x 20*60+50*x=40(60+x) 1200+50x=2400+40x 50x-40x=2400-1200 10x=1200 /10 x=120 gallons 50 % Antifreeze
 Percentage-and-ratio-word-problems/437599: how many gallons of a 90% antifreeze solution must be mixed with 90 gallons of 15% antifreeze to get a mixture that is 80% antifreeze?1 solutions Answer 302724 by mananth(12270)   on 2011-04-18 20:54:09 (Show Source): You can put this solution on YOUR website!------ Percent ---------------- quantity Antifreeze 15 ----------------90 Antifreeze 90 ----------------x Total 80 ---------------- 90 + x 15*90+90*x=80(90+x) 1350+90x=7200+80x 90x-80x =7200-1350 10x=5850 /10 x=585 gallons 90 % Antifreeze
 Radicals/437595: sqrt (a^3)1 solutions Answer 302718 by mananth(12270)   on 2011-04-18 20:48:32 (Show Source): You can put this solution on YOUR website! OR can be written as
 Travel_Word_Problems/437587: a plane flys 420 miles with the wind and 350 miles against the wind at the same length of time with a wind speed of 20 miles per hour what is the speed of the plane1 solutions Answer 302714 by mananth(12270)   on 2011-04-18 20:44:18 (Show Source): You can put this solution on YOUR website!plane speed x mph wind speed 20 mph .. against wind x-20 mph with wind x+20 mph Distance against wind 350 Distance with tail wind 420 Time = same 350/(x- 20)=420/(x+20) 350*(x+20)=420*(x-20) 350x+7000=420x -8400 420x-350x=8400+ 7000 70x=15400 /70 x= 220 mph
 Travel_Word_Problems/437577: Flying against a headwind, a plane covers 900 miles in 2 hours. The return trip with a tailwind only takes an hour and a half. Find the speed of the wind, and the speed of the plane within the air mass.1 solutions Answer 302707 by mananth(12270)   on 2011-04-18 20:39:25 (Show Source): You can put this solution on YOUR website!against wind 2.00 hours with wind 1.50 hours Distance = same=900 plane speed =x wind speed =y t=d/r 900/(x-y)=2.00 2(x-y)= 900.00 2x-2y=900 ....................1 900/(x+y)=1.50 1.50(x+ y)=900 1.50x+1.50y=900 ...............2 Multiply (1) by 1.50 Multiply (2) by 2.00 we get 3x-3y=1350 3x+3y=1800 6x=3150 /6 x=525mph plane speed plug value of x in (1) 2x-2y=900 1050-2y =900 -2y=900-1050 -2y=-150 y=75 mph wind speed
 test/437259: Solve. A boat moves 5 kilometers upstream in the same amount of time it moves 17 kilometers downstream. If the rate of the current is 8 kilometers per hour, find the rate of the boat in still water. A. 7 1/12 kilometers per hour B. 3 1/3 kilometers per hour C. 8 kilometers per hour D. 14 2/3 kilometers per hour 1 solutions Answer 302450 by mananth(12270)   on 2011-04-18 09:13:07 (Show Source): You can put this solution on YOUR website!Boat speed x mph current speed 8 mph .. against current x- x - 8 mph with current x+ x + 8 mph Distance against wind 5 Distance with tail wind 17 Time = same 5 /(x- 8 )= 17 /(x+ 8 ) 5 *(x+ 8 )= 17 *(x- 8 ) 5 x + 40 = 17 x -136 17 x -5 x = 136 + 40 12 x = 176 / 12 x= 14.67 mph option D
 test/437276: Write an equation in point slope form of the line that passes through the given points ( -3, 1/2) ; (-7,5/2)1 solutions Answer 302448 by mananth(12270)   on 2011-04-18 09:02:45 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 -3 0.5 -7 2.5 slope m = (y2-y1)/(x2-x1) -0.5 m= -0.5 Plug value of the slope and point ( -3 , 0.5 ) in Y = m x + b 0.50 = 1.5 + b b= 0.5 1.5 b= -1 So the equation will be Y = -0.5 x + -1