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# Recent problems solved by 'mananth'

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 Quadratic_Equations/498174: During the first part of a trip, a canoiest travels 35 mls. at a certain speed. The canoiest travels 9 mls. on the second part of the trip. at a speed of 5 mls. slower. The total time for this trip is 2 hrs. What was the speed on each part of the trip?1 solutions Answer 336928 by mananth(12270)   on 2011-09-15 02:39:57 (Show Source): You can put this solution on YOUR website!first part 35 miles second part 9 miles speed in first part x mph speed second part x -5 mph Total rowing time 2 hours Time first part 35 / x Time second part 9 / ( x -5 ) Time first part + time second part = 2 hours 35 / x + 9 /(x -5 ) = 2 LCD = ( x + 0 )* (x -5 ) multiply the equation by the LCD we get 35 * (x -5 )+ 9 x = 2 35 x -175 + 9 x = 2 X^2 + -10 x 54 x -175 = 2 X^2 2 X^2 -54 x 175 = 0 2 X^2+ -54 x+ 175 = / 2 1 X^2 -27 x 87.5 = Find the roots of the equation by quadratic formula a= 1 b= -27 c= 87.5 b^2-4ac= 729 - -350 b^2-4ac= 379 = 19.47 x1=( 27 + 19.47 )/ 2 x1= 23.23 mph x2=( 27 -19.47 ) / 2 x2= 3.77 mph First Part speed = 23.23 mph Second part speed = 18.23 mph m.ananth@hotmail.ca
 Money_Word_Problems/498162: kate invests money in two plans. She invests three-fifths of the money in an account at a return rate of 2%. She invests the remainder of the money in an account with a return rate of 4%. If the total interest earned in one year from investments is \$84,00, how much was invested in each plan?1 solutions Answer 336927 by mananth(12270)   on 2011-09-15 02:28:52 (Show Source): You can put this solution on YOUR website!let total money invested be x 3x/5 ----------- 2% 2x/5-------------4% interest 3x/5 * 0.02 + 2x/5* 0.04 = 84 0.06x/5 +0.08x/5 = 84 0.14x=5*84 0.14x=420 x= 420/0.14= 3000 2%----------- 3*3000/5 = 1800 4%------------2*3000/5 = 1200 m.ananth@hotmail.ca
 Points-lines-and-rays/498168: A 4ft by 8ft rectangle has an area of _____ft^2. 1 solutions Answer 336925 by mananth(12270)   on 2011-09-15 02:05:52 (Show Source): You can put this solution on YOUR website!32ft^2
 Linear-systems/498172: Solve the stem of linear equations. What is the x and y answer to this problem? 2x + y = 4 x - y = 2 1 solutions Answer 336924 by mananth(12270)   on 2011-09-15 02:05:03 (Show Source): You can put this solution on YOUR website!2 x + 1 y = 4 .............1 1 x -1 y = 2 .............2 Eliminate y multiply (1)by 1 Multiply (2) by 1 2 x 1 y = 4 1 x -1 y = 2 Add the two equations 3 x = 6 / 3 x = 2 plug value of x in (1) 2 x + 1 y = 4 4 + 1 y = 4 1 y = 4 -4 1 y = 0 y = 0
 Linear-systems/498173: Solve the stem of linear equations. What is the x and y answer to this problem? y - 2x = 0 6y + 2x = 01 solutions Answer 336923 by mananth(12270)   on 2011-09-15 02:03:30 (Show Source): You can put this solution on YOUR website!-2 x + 1 y = 0 2 x + 6 y = 0 Eliminate y multiply (1)by -6 Multiply (2) by 1 12 x -6 y = 0 2 x 6 y = 0 Add the two equations 14 x = 0 / 14 x = 0 plug value of x in (1) -2 x + 1 y = 0 0 + 1 y = 0 1 y = 0 1 y = 0 y = 0
 Mixture_Word_Problems/497543: Manuel traveled 5 hours nonstop to mexico, a total of 293 miles. He took a train part of the way, which averaged 70mph, and then took a bus the remaining distance, which averaged 40mph. how long was manuel on the train?1 solutions Answer 336752 by mananth(12270)   on 2011-09-14 10:19:33 (Show Source): You can put this solution on YOUR website!Train x miles --------- 70 mph Bus 293-x miles---------40 mph time train + time bus = 5 t=d/r x/70 + (293-x)/40 = 5 Multiply by LCD 2800 40x+70(293-x)= 5 * 2800 -30x+20510=14000 -30x=-6510 x=-6510/-30 x=217----------- train distance balance bus distance m.ananth@hotmail.ca
 Mixture_Word_Problems/497536: Shanika has invested in 3 different stocks. Stock A is currently worth \$4.50 per share. Stock B is worth \$7.00 per share, while stock C is worth \$10.00 per share. Shanika purchased half as many shares of stock B as stock A and half as many shares of stock C as stock B. If her total investments are currently worth %546, how many shares of each stock does she own?1 solutions Answer 336750 by mananth(12270)   on 2011-09-14 10:09:57 (Show Source): You can put this solution on YOUR website!Stock A = x-----------------4.50 Stock B = x/2---------------7.00 Stock C = x/4---------------10.00 Total investment = 546 4.5x+7*(x/2)+10*(x/4)=546 multiply by 4 18x+14x+10x=2184 42x=2184 x=52 ----------- A 26----------------B 13----------------C CHECK 52*4.5+26*7+13*10=546 m.ananth@hotmail.ca
 Money_Word_Problems/497529: A sum of \$2,450 is invested, part of it at 11% interest and the remainder at 14%. If the interest earned by the 14% investment is \$100 more than the interest earned by the 11% investment, find the amount invested at each rate. Can you show work??1 solutions Answer 336748 by mananth(12270)   on 2011-09-14 09:44:30 (Show Source): You can put this solution on YOUR website!Part I 11.00% per annum ------------- x Part II 14.00% per annum ------------ y total investment 2450 Interest----- 11.00% x Interest = 14.00% y greater by 100 11.00% x = 14.00% y + 100 multiply by 100 11 x - 14 y = 10000 --------1 x + y = 2450 -------- 2 eliminate y Multiply 1 by 1 Multiply 2 by 14 we get 11 x -14 y = 10000 14 x +14 y = 34300 25 x = 44300 / 25 x= 1772 Plug the value of x in in 1 19492 -14 y = 10000 -14 y = 10000 -19492 -14 y = -9492 / -14 y= 678 \$ 1772 at 11.00% \$ 678 at 14.00%
 Mixture_Word_Problems/497522: how much of a 60% orange juice drink must be mixed with 4 gallons of a 30% orange juice drink to obtain a mixture of 50% orange juice?1 solutions Answer 336743 by mananth(12270)   on 2011-09-14 09:23:40 (Show Source): You can put this solution on YOUR website! percent ---------------- quantity Orange juice I 30 ---------------- 4 gallons Orange juice II 60 ---------------- x gallons Mixture 50 ---------------- 4 + x gallons 30 * 4 + 60 x = 50 ( 4 + x ) 120 + 60 x = 200 + 50 x 60 x + -50 x = 200 - -120 10 x = 80 / 10 x = 8 8 gallons of 60 % Orange juice II II
 Travel_Word_Problems/497518: A bird travels at 500 mph and leaves 10 minutes before his bird friend, which travels at 1500 mphs. How long does it take the friend bird to catch up to the bird that left 10 minutes before him? ... ANSWER NOW IM CURRENTLY IN MY MATH CLASS AND IN BIG TROUBLE IF YOU DONT ANSWER THIS!!1 solutions Answer 336742 by mananth(12270)   on 2011-09-14 09:20:26 (Show Source): You can put this solution on YOUR website!Bird I 500 mph Bird II 1500 mph In 10 minutes = 1/6 hour bird I travels 500*1/6 = 83.33 miles. difference between their speeds = 1000 d= 83.33 speed = 1000 mph time = d/r 83.33/1000 0.0833 hours 0.0833*3600= 300 seconds time to catchup = 300 seconds
 Mixture_Word_Problems/497497: How much 10% acid solution and 30% acid solution should be mixed together to yield 100 liters of a 25% acid solution?1 solutions Answer 336741 by mananth(12270)   on 2011-09-14 09:14:23 (Show Source): You can put this solution on YOUR website!acid percentage ---------------- quantity Acid I 10 ---------------- x liters Acid II 30 ---------------- 100 - x liters Mixture 25.00% ---------------- 100 10x+30(100-x)=25 * 100 10x +3000 -30x= 2500 10x-30x =2500 - 3000 -20 x= -500 / -20 x=25 liters 10.00% Acid I 75 liters 30.00% Acid II
 Mixture_Word_Problems/497505: How much 10% acid solution and 30% acid solution should be mixed together to yield 100 liters of a 25% acid solution?1 solutions Answer 336740 by mananth(12270)   on 2011-09-14 09:12:22 (Show Source): You can put this solution on YOUR website!percent percentage ---------------- quantity Acid I 10 ---------------- x liters Acid II 30 ---------------- 100 - x liters Mixture 25.00% ---------------- 100 10x+30(100-x)=25 * 100 10x +3000 -30x= 2500 10x-30x =2500 - 3000 -20 x= -500 / -20 x=25 liters 10.00% Acid I 75 liters 30.00% Acid II
 Angles/497510: An angle is 20 degrees more than four time its complement, how do I figure this out? I know what a complement is, I just don't know how to figure this problem out since I wasn't given an original degree. Also: Find the supplement of angle A if m(A = 3x + 50. How do I figure this out as well? I am not looking for the answer, unless you are going to provide me with detailed steps with it. I am looking for an explanation on how to figure it out this way I can figure out other similar problems! Please don't just hand me an answer I need steps and thorough explanations that I can understand! Thank you! 1 solutions Answer 336739 by mananth(12270)   on 2011-09-14 09:02:09 (Show Source): You can put this solution on YOUR website!let angle be x complement = (90-x) 4 times = 4 (90-x) 20 more x= 4(90-x)+20 x=360-4x+20 5x=380 x=76 m(A) = 3x+50 supplement = 180-(3x+50) =180-3x-50 =130-3x ... CHECK add them up you get 180 deg
 Travel_Word_Problems/497459: a boat travel 10 kilometer. upstream and 10 kilometer. back. the trip upstream and back takes 1.5 hours. If the speed of the current is 5 kilometer. per hour what is the speed of the boat in still water1 solutions Answer 336736 by mananth(12270)   on 2011-09-14 05:41:50 (Show Source): You can put this solution on YOUR website!Boat speed x current speed 5 against current x- 5 kph with current x+ 5 kph Distance= 10 km Time against + time with = 1.5 hours 10 /( x + 5 ) + 10 /(x - 5 ) = 1.5 LCD = (x - 5 ) ( x + 5 ) 10 *( x - 5 ) + 10 (x + 5 ) = 1.5 10 x - 50 + 10 x + 50 = 1.5 ( x ^2 - 25 ) 20 x = 1.5 x ^2 - 37.5 1.5 x ^2 - -20 x - 37.5 Find the roots of the equation by quadratic formula a= 1.5 , b= -20 , c= -37.5 b^2-4ac= 400 + 225 b^2-4ac= 625 x1=( 20 + 25 )/ 3 x1= 15 x2=( 20 -25 ) / 3 x2= -1.67 Ignore negative value 15 mph=speed of boat m.ananth@hotmail.ca
 Travel_Word_Problems/497378: A freight train leaves a station and travels north at 55 mph. Four hours later, a passenger train leaves on a parallel track and travels north at 66 mph. How long will it take the passenger train to overtake the freight train?1 solutions Answer 336714 by mananth(12270)   on 2011-09-13 23:45:03 (Show Source): You can put this solution on YOUR website!Freight train 55 mph Passenger train 66 mph Freight train 02:00 Passenger train 06:00 Difference in time= 04:00 => 4 hours Freight train will have covered 220 miles before Passenger train starts from station catch up distance= 220 miles catch up speed = 66 -55 mph catch up speed = 11 mph Catchup time = catchup distance/catch up speed catch up time= 220 / 11 catch up time= 20 hours m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/497240: Represent the number whose tens' digit is t and whose units digit is u. I have no idea what the answer is that he is looking for. Is this close and if not what is the answer? 30=t 5=u 1 solutions Answer 336697 by mananth(12270)   on 2011-09-13 21:18:11 (Show Source): You can put this solution on YOUR website!The number will be 10t+u
 Problems-with-consecutive-odd-even-integers/496721: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. -2x + 6y = -12 x + 3y = -3 1 solutions Answer 336536 by mananth(12270)   on 2011-09-13 09:22:45 (Show Source): You can put this solution on YOUR website!-2 x + 6 y = -12 .............1 1 x + 3 y = -3 .............2 Eliminate y multiply (1)by 1 Multiply (2) by -2 -2 x 6 y = -12 -2 x -6 y = 6 Add the two equations -4 x = -6 / -4 x = 1.50 OR 1 1/ 2 plug value of x in (1) -2 x + 6 y = -12 -3 + 6 y = -12 6 y = -12 + 3 6 y = -9 y = -1.50 OR m.ananth@hotmail.ca
 Problems-with-consecutive-odd-even-integers/496722: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this. -3x + 4y = -19.5 -3x + y = -10.5 1 solutions Answer 336535 by mananth(12270)   on 2011-09-13 09:20:40 (Show Source): You can put this solution on YOUR website!-3 x + 4 y = -19.5 .............1 -3 x + 1 y = -10.5 .............2 Eliminate y multiply (1)by 1 Multiply (2) by -4 -3 x 4 y = -19.5 12 x -4 y = 42 Add the two equations 9 x = 22.5 / 9 x = 2.50 OR 2 1/ 2 plug value of x in (1) -3 x + 4 y = -19.5 -7.5 + 4 y = -19.5 4 y = -19.5 + 7.5 4 y = -12 y = -3 (5/2,-3)
 Problems-with-consecutive-odd-even-integers/496723: Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this. -x + 6y = 54 3x + y = 9 1 solutions Answer 336534 by mananth(12270)   on 2011-09-13 09:18:14 (Show Source): You can put this solution on YOUR website!-1 x + 6 y = 54 .............1 1 y = 9 -3 x ---------2 / 1 = y = 9 -3 x Substitute y in (1) -1 x + 6 ( 9 -3 x ) = 54 -1 x + 54 + -18 x = 54 -1 x -18 x = 54 -54 -19 x = 0 / -19 x= 0 Plug the value of x in (1) -1 x + 6 y = 54 -1 * 0 + 6 y = 54 0 + 6 y = 54 6 y = 54 / 6 y= 9 Solution (0,9) m.ananth@hotmail.ca
 Numbers_Word_Problems/496725: write the english phrase as an algebraic expression, then simplify the expression. Let x represent the number. seven increased by the product of 2 and one less than a number1 solutions Answer 336533 by mananth(12270)   on 2011-09-13 09:14:55 (Show Source): You can put this solution on YOUR website!2(x-1)+7
 Travel_Word_Problems/492720: two automobiles set out simultaneously from places 100 miles apart. they traveled toward each other and passed at the end of 1 hour and 40 minutes. the speed of one automobile was 5 miles per hour greater than of the other. find the speed of each. can you please answer it for me? thanks!1 solutions Answer 335164 by mananth(12270)   on 2011-09-07 06:20:39 (Show Source): You can put this solution on YOUR website!Distance they meet from one car = x other car travels 100-x miles when they meet. distance/time = speed 1 h 40 mins = 1 2/3 hours = 5/3 hours x/(5/3) -(100-x)/(5/3)= 5 3x/5 - 3(100-x)/5 =5 (3x-300+3x)/5 = 5 6x-300=25 6x= 325 x=54.16 one car travels 54.16 miles in 5/3 hours so in 1 hour it travels 54.16/(5/3) = 32.5 mph second car travels 100-54.16 = 45.84 mile speed = 45.84/(5/3)= 27.5 mph cheers
 Linear-equations/492683: (3y-13)+(y+33)=1801 solutions Answer 335163 by mananth(12270)   on 2011-09-07 06:06:35 (Show Source): You can put this solution on YOUR website!(3y-13)+(y+33)=180 3y+y-13+33=180 4y+20=180 4y=180-20 4y=160 /4 y= 40
 Linear-equations/492700: Find an equation for the line that passes through the given points. (-5,0) and (1,30)1 solutions Answer 335162 by mananth(12270)   on 2011-09-07 06:02:28 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 -5 0 1 30 slope m = (y2-y1)/(x2-x1) ( 30 - 0 )/( 1 - -5 ) ( 30 / 6 ) m= 5 Plug value of the slope and point (-5 ,0) in Y = m x + b 0.00 = -25 + b b= 0 - -25 b= 25 So the equation will be Y = 5 x + 25 m.ananth@hotmail.ca
 Travel_Word_Problems/492691: a man drove from his home to the airport at a distance of 40 miles and then returned home on the same way. the round trip took 2 hours. his speed on the return trip was 30 miles/hr faster than his speed in going. what was his rate of speed on the trip from his home.1 solutions Answer 335152 by mananth(12270)   on 2011-09-07 02:07:14 (Show Source): You can put this solution on YOUR website!Time to airport + time to home = 2hours d=40 going speed=x returning speed= x+30 Multiply by the LCD x(x+30) 40(x+30)+40x= 2x(x+30) 40x+1200+40x=2x^2+60x 2x^2-80x+60x-1200=0 2x^2-20x-1200=0 /2 x^2-10x-600=0 (x-30)(x+20)=0 x= 30 the speed while going to airport
 Percentage-and-ratio-word-problems/492615: What quantity of 80 per cent acid solution must be mixed with a 25 percent solution to produce 660 mL of a 50 per cent solution? 1 solutions Answer 335151 by mananth(12270)   on 2011-09-07 01:55:22 (Show Source): You can put this solution on YOUR website!percent percentage ---------------- quantity Acid I 80 ---------------- x ml Acid II 25 ---------------- 660 - x ml Mixture 50.00% ---------------- 660 80 x + 25 ( 660 - x ) = 50 * 660 80 x + 16500 - 25 x = 33000 80 x - 25 x = 33000 - 16500 55 x = 16500 / 55 x= 300 ml 80.00% Acid I 360 ml 25.00% Acid II
 Mixture_Word_Problems/492605: Kiera wants to make a solution that is 60% Alcohol. How many liters of a 70% Alcohol solution should Kiera add to 12 liters of a 45% Alcohol solution to achieve her goal?1 solutions Answer 335150 by mananth(12270)   on 2011-09-07 01:49:29 (Show Source): You can put this solution on YOUR website!---------------- percent ---------------- quantity Alcohol I 45 ---------------- 12 liters Alcohol II 70 ---------------- x liters Mixture 60 ---------------- 12 + x liters 45 * 12 + 70 x = 60 ( 12 + x ) 540 + 70 x = 720 + 60 x 70 x + -60 x = 720 - -540 10 x = 180 / 10 x = 18 18 liters of 70 % Alcohol
 Linear-equations/492603: line parallel to the line y = 2x + 5 and through the point (2,-3) whats the answer1 solutions Answer 335149 by mananth(12270)   on 2011-09-07 01:46:04 (Show Source): You can put this solution on YOUR website!Find the slope of this line y = 2 x + 5 Divide by 1 y = 2 x + 5 Compare this equation with y=mx+b slope m = 2 The slope of a line parallel to the above line will be the same The slope of the required line will be 2 m= 2 ,point (2,-3) Find b by plugging the values of m & the point in y=mx+b -3 = 4.00 + b b= -7 m= 2 Plug value of the slope and b in y = mx +b The required equation is y = 2 x -7 y = 2 x -7 m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/492676: how can you find the slope and y-intercept of the line y= -2/9x-61 solutions Answer 335147 by mananth(12270)   on 2011-09-07 01:40:40 (Show Source): You can put this solution on YOUR website!y= -2/9x-6 compare this equation with y=mx+b m=-2/9 & c=-6 y intercept =-6
 Square-cubic-other-roots/492622: what is 1 solutions Answer 335129 by mananth(12270)   on 2011-09-07 00:01:58 (Show Source):
 Rectangles/492626: a room is 15 feet by 30 feet and the tile 1 foot and cost 92 cent how much will it cost to cover the entire room1 solutions Answer 335125 by mananth(12270)   on 2011-09-06 23:59:24 (Show Source): You can put this solution on YOUR website!area of room /area of tile = number of tiles number of tiles * cost per tile = Total cost of tiling. 15*30 = 450 sq.ft tile area = 1*1=1 sq.ft 450/1 = 450 tiles 450 *0.92 = \$414
 Exponents/492636: Multiply (-3n)^2(2n^9)^2 I can never remember what to do with exponents like this. Multiply or add? Any help will be greatly appreciated1 solutions Answer 335123 by mananth(12270)   on 2011-09-06 23:55:15 (Show Source): You can put this solution on YOUR website!When it is a multiplication the exponents have to be added. (-3n)^2(2n^9)^2 (9n^2)(4n^18) 36n^20