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# Recent problems solved by 'mananth'

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 Mixture_Word_Problems/576724: Two sisters shared a \$36 5000 inheritance. Teri invested her share at 9%, while Tammy obtained 8.5% interest. After on year, their combined interest was 3200. How much did each sister invest? 1 solutions Answer 369990 by mananth(12270)   on 2012-02-23 01:15:56 (Show Source): You can put this solution on YOUR website!I think the inheritance must be \$36,500 and not 365,000 Teri 9.00% per annum ---x Tammy 8.50% per annum ---y x+y= 36500 ------------------------1 9.00%x+8.50%y= 3200 Multiply by 100 9x+8.5y=320000.00 --------2 Multiply (1) by -9 we get -9 x -9 y= -328500.00 Add this to (2) 0 x -0.5 y= = -8500 divide by -0.5 y=17000 investment at 8.50% Balance 19500 investment at 9.00% CHECK 17000 --------- 8.50% ------- 1445.00 19500 ------- 9.00% ------- 1755.00 Total -------------- 3200.00
 Miscellaneous_Word_Problems/576747: how whould you write x equals the sum of the square root of 225 and the quotient of 15 and31 solutions Answer 369985 by mananth(12270)   on 2012-02-23 00:25:14 (Show Source):
 Polygons/576757: using the ratios 24/32 = 6/(x -1) or 24(x -1) =32 x 6 solve for x Can you please explain so I can do the other questions thank you.1 solutions Answer 369984 by mananth(12270)   on 2012-02-23 00:15:59 (Show Source): You can put this solution on YOUR website!24(x -1) =32 *6 24x-24 =192 +24 24x=192+24 24x=216 /24 x=9
 Money_Word_Problems/576764: Ann invested her savings in two investment funds. The 6000 that she invested in Fund A returned a 5% profit. The amount that she invested in Fund B returned a 1% profit. How much did she invest in Fund B, if both funds together returned a 4% profit? 1 solutions Answer 369982 by mananth(12270)   on 2012-02-23 00:13:23 (Show Source): You can put this solution on YOUR website! percent ---------------- Amount \$ Fund A 5 ---------------- 6000 Fund B 1 ---------------- x Total 4 ---------------- 6000 + x 5*6000 +1x=4(6000+x) 30000 + 1x = 24000 +4x x-4x=-30000+24000 -3x=-6000 /-3 x=2000 \$2000 in Fund B m.ananth@hotmail.ca Check 2000@1%=20 6000@6%= 300 Total 320 320 of 8000 = 320/8000 *100 = 4%
 Human-and-algebraic-language/576591: The manger of a farmer's market has 500lb of gain that cost 1.20 per pound. How many pounds of meal costing .80 per pound should be mixed with the 500lb of grain to produce a mixture that cost 1.05 per pound?1 solutions Answer 369933 by mananth(12270)   on 2012-02-22 20:35:00 (Show Source): You can put this solution on YOUR website! --------price ---------------- quantity Grain 1.2 ---------------- 500 lb Meal 0.8 ---------------- x lb Mixture 1.05 ---------------- 500 + x lb 1.2*500+0.8x=1.05(500+x) 600+0.8x=525+1.05x 0.8x-1.05x=-600 +525 -0.25 x = -75 / -0.25 x = 300 300 lb of Meal m.ananth@hotmail.ca
 Travel_Word_Problems/576149: Without any wind an airplane flies at 200 miles per hour. It travels 800 miles into the wind and then returns with the wind in a total time of 8 hours and 20 minutes. Find the average speed of the wind?1 solutions Answer 369745 by mananth(12270)   on 2012-02-22 01:31:48 (Show Source): You can put this solution on YOUR website!Plane speed = 200 m/h Wind speed = x m/h against wind =200-x with wind =200 +x Total distance =800 miles Total Time= 8.30 hours Time upstream + time downstream =8.3 hours 800/(200-x)+800/(200+x)=8.3 800(200 +x)+800 (200-x)=8.30(40000-X^2 ) 160000+ 800x+160000-800x=332000 -8.3X^2 320000 --332000=-8.3 X^2 12000 =8.3 X^2 x= x= 38.02 mph
 Triangles/576106: In the right triangle the ratio of the measures of three sides are 2 4 8, and its perimeter is 280 inches. find the length to the longest side.1 solutions Answer 369744 by mananth(12270)   on 2012-02-22 00:47:28 (Show Source): You can put this solution on YOUR website!the sides are in the ration 2:4:8 let the common multiple be x the sides are 2x , 4x,8x perimeter = 280 2x+4x+8x=280 14x=280 /14 x= 20 The length of the largest side = 8x = 8*20 =160 in
 Linear-equations/576117: write an equation in the slope-intercept form and then find the slope and y-intercept of the corresponding line. 5x+8y-24=01 solutions Answer 369743 by mananth(12270)   on 2012-02-22 00:43:57 (Show Source): You can put this solution on YOUR website!5x+8y-24=0 8y=--5x+24 /8 y= (-5/8)x+3 compare with y= mx +b m=slope = (-5/8) b= y intercept = 3
 Linear-equations/576139: Write an equation in standard form for the line perpendicular to 8x+y=5 that passes through the point (3, 4)1 solutions Answer 369740 by mananth(12270)   on 2012-02-22 00:40:57 (Show Source): You can put this solution on YOUR website!8 x + 1 y = 5 Find the slope of this line 1 y = -8 x + 5 Divide by 1 y = -8 x + 5 Compare this equation with y=mx+b, m= slope & b= y intercept slope m = -8 The slope of a line perpendicular to the above line will be the negative reciprocal 1/8 m1*m2=-1 The slope of the required line will be 1/8 m= 1/8 ,point ( 3 , 4 ) Find b by plugging the values of m & the point in y=mx+b 4 = 3/ 8 + b b= 29/8 m= 1/8 The required equation is y = 1/ 8 x +29/ 8 m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/576143: 3X2-5X-2/6X3+2X2+3X+1 1 solutions Answer 369736 by mananth(12270)   on 2012-02-22 00:36:36 (Show Source): You can put this solution on YOUR website! factorize the numerator & denominator
 test/575570: (a^2-36)/(a^2+9a+18)1 solutions Answer 369549 by mananth(12270)   on 2012-02-21 08:20:44 (Show Source):
 Rectangles/575609: The perimeter of a rectangle is 56 inches. The ratio of the length to the width is 6:1. What is the length and the width.1 solutions Answer 369548 by mananth(12270)   on 2012-02-21 08:16:12 (Show Source): You can put this solution on YOUR website!ratio of length to width is 6:1 let the commoon multiple be x length = 6x width =x Perimeter = 2(L+W) 2(6x+x) = 56 7x= 56/2 7x=28 /7 x= 4 so length = 6x= 6*4 24 in Width = x = 4 2*4 + 24*2= 56
 Money_Word_Problems/575599: how can \$54000 be invested, part at 12%annual simple interest and the remainder at 6%.so that the interest earned by the two accounts will be eqaul 1 solutions Answer 369546 by mananth(12270)   on 2012-02-21 08:12:36 (Show Source): You can put this solution on YOUR website!let investment @ 12% be x and 6 % be y x+y = 54000...................1 12%x=6*%y multiply by 100 12x=6y x= y/2 substitute x in (1) y/2 + y =54000 multiply by 2 y+2y= 108000 3y=108000 /3 y=36000 \$36,000 @ 6% \$18000 @ 12 %
 Money_Word_Problems/575600: a farmer borrow \$3800 for 9 months from a bank. The discounted the loan at 7% I know that interest is \$199.50 and amount of money the farmer recieved is \$3600.50, but can't figure out the actual interest rate which is 7.39% 1 solutions Answer 369545 by mananth(12270)   on 2012-02-21 08:06:10 (Show Source): You can put this solution on YOUR website!I= p*n*r I= 3800*3/4 * r 199.5 = (3800-199.5) * 3/4*r r= (199.5*4)/(3*3600.50) r=0.07387 r= 7.387% round off
 Complex_Numbers/575604: what is the square root of -144? 1 solutions Answer 369544 by mananth(12270)   on 2012-02-21 07:57:32 (Show Source): You can put this solution on YOUR website! =i*12 =12i
 Evaluation_Word_Problems/575601: George Stoia earns \$1,000 per month plus 5% commission on the amount of sales. George's goal is to earn a minimum of \$2,300 per month. What amount of sales will enable George to earn \$2,300 or more per month? \$ or more 1 solutions Answer 369543 by mananth(12270)   on 2012-02-21 07:54:44 (Show Source): You can put this solution on YOUR website!let the sales amount be x I>=1000 + 5% * x 2300>=1000 +0.05x -1000 1300>=0.05x /0.05 1300/0.05>x 26000>=x Sales should be greater than or equal to \$26,000
 Square-cubic-other-roots/574504: I need help, I have tried this question several times and still am not getting it right. During the first part of a trip, a canoeist travels 55 miles at a certain speed. The canoeist travels 4 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip?1 solutions Answer 369119 by mananth(12270)   on 2012-02-18 03:28:54 (Show Source): You can put this solution on YOUR website!First part 55 miles Second part 4 miles First part x mph Second part x -5 mph Total time 5 hours First part time 55 / x Second part time 4 / ( x -5 ) Time first part + time second part = 5 hours 55 / x + 4 /(x -5 ) = 5 LCD = ( x + 0 )* (x -5 ) multiply the equation by the LCD we get 55 * (x+ -5 )+ 4 x = 5 55 x+ -275 + 4 x = 5 X^2 -25 x 84 x+ -275 = 5 X^2 5 X^2 -84 x+ 275 = 0 5 X^2+ -84 x+ 275 = = 0 / 5 5 X^2 -84 x+ 275 = 0 Find the roots of the equation by quadratic formula a= 5 b= -84 c= 275 b^2-4ac= 7056 - 5500 b^2-4ac= 1556 = 39.45 5 x1=( 84 + 39.45 )/ 10 x1= 12.34 x2=( 84 -39.45 ) / 10 x2= 4.46 Ignore x2 x = 12.34 mph CHECK Time first part + Time second part 4.46 + 0.51 = 4.96 m.ananth@hotmail.ca
 Travel_Word_Problems/574461: during the first part of the trip a canoeist travels 40 miles at a certain speed the canoeist travels 20 miles on the seconf part of the trip at a speed 5 mph slower the total time for the trip is 3 hours what was the speed on each part of the trip?1 solutions Answer 369105 by mananth(12270)   on 2012-02-18 01:38:33 (Show Source): You can put this solution on YOUR website!Forward 40 miles Returning speed to DC 20 miles Forward speed x mph return speed x-5 mph Total time =3hours Time forward 40 / x time return 20/(x-5) add up the time =3 hours 40/x + 20/(x-5)=3 LCD = (x)*(x-5) multiply the equation by the LCD we get 40*(x-5 )+20x = 3 40x-200 +20x=3x^2-15x 75x-200 =3x^2 3x^2-75x+200= 0 3X^2-75 x+200 = 0 Find the roots of the equation by quadratic formula a= 3 b= -75 c= 200 b^2-4ac= 5625 - 2400 b^2-4ac= 3225 = 56.79 2.99 x1=( 75 + 56.79 )/ 6 x1= 21.96 x2=( 75 -56.79 ) / 6 x2= 3.04 Forward speed = 22 mph return speed = 17 mph
 Square-cubic-other-roots/573499: I don't undertand how to simplify radical expressions.I am in Algebra 2 and the problem is as follows: Find the cubed root of (x^6/250). I was brainstorming and I know that 125*2=250 and 125 is a perfect cubed root, but I dont know if that is relevant. I would be really thankful if you could help me solve this problem. Thanks you so much!1 solutions Answer 368784 by mananth(12270)   on 2012-02-15 20:26:32 (Show Source):
 Mixture_Word_Problems/573496: how many cups of 20% alcohol solution and 15% alcohol solution should be mixed in order to make 8 cups of 18% alcohol solution? My try: x+y=8, (x-x+y=8-x)= y+8-x Let x=0.20 Let y=0.15 0.20x+0.15y= 0.18(8) 0.20x+0.15(8-x)=0.18(8) 0.20x+1.2-0.15x=1.44 0.35x+1.2=1.44 -1.2 -1.2 0.35x=0.24 x=0.681 solutions Answer 368782 by mananth(12270)   on 2012-02-15 20:23:39 (Show Source): You can put this solution on YOUR website!percent ----------------quantity Alcohol type I 20.00% ----------------x cups Alcohol type II 15.00% ------ 8-x cups Mixture 18.00% ---------------- 8 20.00%x+15.00%(8-x)= 18.00% * 8 20x+15( 8-x)=144 20x+120 -15x=144 20x-15x=144-120 5 x = 24 / 5 x= 4.8 cups 20.00% Alcohol type I 3.2 cups 15.00% Alcohol type II m.ananth@hotmail.ca
 Graphs/573457: I need help solving this equation! 2x - 7y is less than or equal to 4 I have to get it to the slope-intercept form so I can graph it and I'm stuck, looking for the 'B' part in y=mx+b. Please help me! Please and thank you. :D1 solutions Answer 368780 by mananth(12270)   on 2012-02-15 20:14:53 (Show Source): You can put this solution on YOUR website!2x - 7y is less than or equal to 4 add -2x to both sides /-7
 Travel_Word_Problems/573464: A car travels at a speed of 48mph, another car leaves one hour later at a speed of 72mph. How long will it take for the second car to catch up to the first car?1 solutions Answer 368777 by mananth(12270)   on 2012-02-15 20:09:46 (Show Source): You can put this solution on YOUR website!speed of first car= 48 mph speed of second car = 72 mph second car leaves 1 hour late. so when second car leaves first car has traveled 48 miles catch up distance = 48 miles same direction so catch up speed = 72-48 = 24 mph t=d/r t=48/24 t= 2 hours catch up time = 2hours
 Miscellaneous_Word_Problems/573473: a ladder is resting against a wall. the top of the ladder touches the wall at height of 9 feet. find the length of the ladder if the length is 3 feet more than its distance from the wall1 solutions Answer 368774 by mananth(12270)   on 2012-02-15 19:54:18 (Show Source): You can put this solution on YOUR website!distance from wall = x length of ladder = x+3 feet height where it touches the wall = 9 The ladder,the floor & the wall form a right triangle. The base is one leg The height is the other leg The ladder acts as the hypotenuse Pythagoras theorem (Hyp)^2= (leg1)^2+ Leg2^2 (x+3)^2=x^2+9^2 x^2+6x+9 = x^2+81 6x+9=81 6x=72 /6 x=12 Length of ladder = 12+3 = 15 feet
 Rate-of-work-word-problems/573479: "there were 39,000 people at a ball game the day's receipts were \$276,000 how many people paid \$14 for reserved seats and how many paid \$5 for general admission?" 1 solutions Answer 368773 by mananth(12270)   on 2012-02-15 19:49:32 (Show Source): You can put this solution on YOUR website!x persons General y persons Reserved 1 x + 1 y = 39000 .............1 5 x + 14 y = 276000 .............2 Eliminate y multiply (1)by -14 Multiply (2) by 1 -14 x -14 y = -546000 5 x + 14 y = 276000 Add the two equations -9 x = -270000.00 / -9 x = 30000 plug value of x in (1) 1 x + 1 y = 39000 30000 + 1 y = 39000 1 y = 39000 -30000 1 y = 9000 y = 9000 30000 persons General 9000 persons Reserved
 Linear-equations/573481: determine how many solutions exist use either elimination or substitution to find the solutions if any y=2x+3 and y= -x-41 solutions Answer 368772 by mananth(12270)   on 2012-02-15 19:43:50 (Show Source): You can put this solution on YOUR website!2 x + 1 y = 3 .............1 1 x + 1 y = -4 .............2 Eliminate y multiply (1)by -1 Multiply (2) by 1 -2 x -1 y = -3 1 x + 1 y = -4 Add the two equations -1 x = -7.00 / -1 x = 7 plug value of x in (1) 2 x + 1 y = 3 14 + 1 y = 3 y = -11 (7,-11) is the solution m.ananth@hotmail.ca
 Systems-of-equations/572995: Is this system of equations consistent? So far everything I came up with says it is not. Please help? x + 3y = 32 -3x + 2y = 8 1 solutions Answer 368624 by mananth(12270)   on 2012-02-15 02:11:00 (Show Source): You can put this solution on YOUR website!1 x + 3 y = 32 .............1 -3 x + 2 y = 8 .............2 Eliminate y multiply (1)by -2 Multiply (2) by 3 -2 x -6 y = -64 -9 x + 6 y = 24 Add the two equations -11 x = -40.00 / -11 x = 40/11 plug value of x in (1) 1 x + 3 y = 32 3.64 + 3 y = 32 3 y = 28.36 -27 1 y = 9.45 y = 104/11 The system has one solution consistent and Independant
 Mixture_Word_Problems/572988: We can't seem to understand the method for putting together the equation on a Mixture Word Problem. The MATH is no problem; only the organization of the equation itself: Two kinds of coffee were blended together, one worth \$6.50 a pound and the other worth \$5.95 a pound. The blend contained ten pounds more than twice as much as the \$5.95 coffee than of the \$6.50 coffee. How much of each kind was used if the value of the blend is \$280.30?1 solutions Answer 368622 by mananth(12270)   on 2012-02-15 01:39:48 (Show Source): You can put this solution on YOUR website!Coffee type A \$6.50 -----------x pounds Coffee type B \$5.95-------------y pounds y=2x+10 6.50x+5.95y=280.30 multiply by 100 650x+595y=28030 -2 x + 1 y = 10 .............1 650 x + 595 y = 28030 .............2 Eliminate y multiply (1)by 595 Multiply (2) by -1 -1190 x 595 y = 5950 -650 x + -595 y = -28030 Add the two equations -1840 x = -22080.00 / -1840 x = 12 plug value of x in (1) -2 x + 1 y = 10 -24 + 1 y = 10 1 y = 34 -27 1 y = 34 y = 34 12 pounds coffee type A 34 pounds Coffee type B m.ananth@hotmail.ca
 Mixture_Word_Problems/572980: how many liters of a 80% acid solution must be mixed with a 10% acid solution to get 560liters of a 70% acid solution 1 solutions Answer 368617 by mananth(12270)   on 2012-02-15 01:17:09 (Show Source): You can put this solution on YOUR website!percent ---------------- quantity Acid solution Type I 80.00% ---------------- x L Acid solution type II 10.00% ------ 560 - x L Mixture 70.00% ---------------- 560 80.00%x+10.00%(560-x)=70.00%*560 80x+10(560-x)= 39200 80x+5600-10x=39200 80x-10x =39200 -5600 70x= 33600 /70 x =480L 80.00% Acid solution Type I 80L 10.00% Acid solution type II
 Length-and-distance/572983: A chauffer can get paid in two different ways. Plan A: \$500 plus \$9/hr. Plan B: \$14/hour Suppose that a job takes "n" hours. For what values of "n" is Plan A better than Plan B? Select Topic: 1 solutions Answer 368614 by mananth(12270)   on 2012-02-15 00:37:23 (Show Source): You can put this solution on YOUR website!Let n be the number of hours Plan A 500 + 9 n Plan B 14 n Plan A > Plan B 500 + 9 n > 14.00 n add -500 to both sides 500 + 9.00 n- -500 > 14.00 n -500 9 n > > 14 n -500 add -14 n -5 n > -500 / -5 n < 100 n should be less than 100 for Plan A to be better than plan B Plan A > Plan B at 80 hours Plan A 500 + 9.00 * 80 = 1220 Plan B 14.00 * 80 = 1120 Plan A < Plan B for 110 hours Plan A 500 + 9.00 * 110 = 1490 Plan B 14.00 * 110 = 1540
 Linear-equations/572982: I need step by step instructions on how to solve the following: Solve by the elimination method. 9x - y = 40 x + 8y = 451 solutions Answer 368608 by mananth(12270)   on 2012-02-15 00:05:42 (Show Source): You can put this solution on YOUR website!9 x + -1 y = 40 .............1 1 x + 8 y = 45 .............2 Eliminate y multiply (1)by 8 Multiply (2) by 1 72 x -8 y = 320 1 x + 8 y = 45 Add the two equations 73 x = 365 / 73 x = 5 plug value of x in (1) 9 x + -1 y = 40 45 + -1 y = 40 -1 y = -5 y = 5 (5,5)
 Linear-equations/572898: Write the equation of the line that passes through the given point and is perpendicular to the given line. Write the answer in slope-intercept form. P(-9, 7), y + 8x = -19 1 solutions Answer 368583 by mananth(12270)   on 2012-02-14 22:24:06 (Show Source): You can put this solution on YOUR website!8x +y = -19 Find the slope of this line y = -8x-19 Compare this equation with y=mx+b, m= slope , & b= y intercept slope m = -8 The slope of a line perpendicular to the above line will be the negative reciprocal 1/8 m1*m2=-1 The slope of the required line will be 1/8 m= 1/8 ,point ( -9 , 7 ) Find b by plugging the values of m & the point in y=mx+b 7 = -9/ 8 + b b= -65/8 m= 1/8 The required equation is y = 1/ 8x-65/ 8 m.ananth@hotmail.ca