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# Recent problems solved by 'mananth'

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 Linear-equations/504347: Find an equation of the line. Write the equation in the standard form. Through (6,8); parallel to 9x-y=61 solutions Answer 339599 by mananth(12270)   on 2011-09-26 00:22:45 (Show Source): You can put this solution on YOUR website!9 x + -1 y = 6 Find the slope of this line make y the subject -1 y = -9 x + 6 Divide by -1 y = 9 x -6 Compare this equation with y=mx+b slope m = 9 The slope of a line parallel to the above line will be the same The slope of the required line will be 9 m= 9 ,point ( 6 , 8 ) Find b by plugging the values of m & the point in y=mx+b 8 = 54.00 + b b= -46 m= 9 Plug value of the slope and b in y = mx +b The required equation is y = 9 x -46 y = 9 x -46 m.ananth@hotmail.ca
 Travel_Word_Problems/504358: If a bus leaves @ 11:45 and travels at 30 mph and then a car leaves at 12:00 and travels @ 45mph when will they meet?1 solutions Answer 339598 by mananth(12270)   on 2011-09-26 00:16:54 (Show Source): You can put this solution on YOUR website!Bus 30 mph Car 45 mph Bus 11:45 Car 12:00 Difference in time= 00:15 => 0.25 hours Bus will have covered 7.5 miles before Car starts from station catch up distance= 7.5 miles catch up speed = 45 -30 mph catch up speed = 15 mph Catchup time = catchup distance/catch up speed catch up time= 7.5 / 15 catch up time= 0.5 hours They will meet at 12:30
 Travel_Word_Problems/504368: At the same time Kris leaves Washington, D.C. for Detroit. Amy leaves Detroit for Washington, D.C.. The distance between the cities is 510 miles. Amy's average speed is 5 mph faster than Kris's. How fast is Kris driving if they pass each others in 6 hours?1 solutions Answer 339596 by mananth(12270)   on 2011-09-26 00:07:08 (Show Source): You can put this solution on YOUR website!Kris x mph Amy x+ 5 mph .. They are moving towards each other So add up their speed. combined speed = x+ x + 5 ( 2 x + 5 ) Time = 6 hours Distance = 510 miles Distance = speed * time ( 2 x +5 )* 6 = 510 12 x + 30 = 510 12 x = 510 + -30 12 x = 480 / 12 x= 40 mph Kris Amy 40 + 5 = 45 mph
 Average/504407: how do i find the lenght of the three pieces? A 56 inch board is to be divided into 3 pieces so that the second piece is twice as long as the first, and the third piece is 4 times as long as the first. Find the length pf all three pieces.1 solutions Answer 339595 by mananth(12270)   on 2011-09-25 23:57:24 (Show Source): You can put this solution on YOUR website!first piece =x second piece = 2x third piece = 4x x+2x+4x=56 7x=56 /7 x=8 first piece =8 second piece = 2x=> 16 third piece = 4x=>32 8+16+32=56
 Average/504402: Please explain this for me. The perimeter of a rectangular billboard is 60 feet and its length is 6 feet longer than its width. Find the dimensions of the billboard.1 solutions Answer 339590 by mananth(12270)   on 2011-09-25 23:53:11 (Show Source): You can put this solution on YOUR website!Perimeter = 60 feet Width = x ft Length ( x + 8 ) Perimeter =2(L+W) Perimeter = 2((x + 8)+ x) Perimeter = 2((x+8+ x) Perimeter = 16 + 2 x 60 = 2 x + 16 60 - = 2 x 60 -16 = 2 x 44 = 2 x x= 22 ft Width Length = 30
 Average/504399: I am very confused please help. Find three consecutive integers whose sum is -114?1 solutions Answer 339589 by mananth(12270)   on 2011-09-25 23:46:36 (Show Source): You can put this solution on YOUR website!let the consequtive integers be x, x+1,x+2 x+x+1+x+2 =-114 3x+3=-114 3x=-114-3 3x=-117 /3 x=-117/3 x=-39 -39,-38,-37
 Travel_Word_Problems/504380: a train leaves a station and travels north at 75 km/h. two hours later a second train leaves on a parallel track and travels north at 125km/h. how far from the station will they meet?1 solutions Answer 339588 by mananth(12270)   on 2011-09-25 23:43:45 (Show Source): You can put this solution on YOUR website!Train A 75 mph Train B 125 mph Difference in time= 04:00 => 4 hours Train A will have covered 300 miles before Train B starts from station catch up distance= 300 miles catch up speed = 125 -75 mph catch up speed = 50 mph Catchup time = catchup distance/catch up speed catch up time= 300 / 50 catch up time= 6 hours Train B speed = 125 mph Time to catch up = 6 hours D=Speed * time D= 125 * 6 D= 750 miles Train B will catch up when it has traveled 750 miles
 Average/504395: Can you please help me solve this? I think the answer is \$1030. Find the interest on a \$2000 loan at 7% for 5 years. 1 solutions Answer 339585 by mananth(12270)   on 2011-09-25 23:28:53 (Show Source): You can put this solution on YOUR website!I = p*n*r p=2000 n=5 r=7%=0.07 I= 2000*5*0.07 I= \$700
 Problems-with-consecutive-odd-even-integers/504394: three times the sum of two consecutive integers is three less than two times the larger integer. find the integers1 solutions Answer 339583 by mananth(12270)   on 2011-09-25 23:25:12 (Show Source): You can put this solution on YOUR website!two consequtive integers x & x+1 3 times the sum => 3(x+x+1)=3(2x+1) larger integer x+1 two times the larger integer => 2(x+1) 3 less=> 2(x+1)-3 3(2x+1)=2(x+1)-3 6x+3=2x+2-3 6x-2x=-3-3+2 4x=-4 x=-1 -1 & 0
 Average/504393: Please help me solve this i am confused. The sum of 6 and twice a number is equal to 7 less than a number. find the number1 solutions Answer 339582 by mananth(12270)   on 2011-09-25 23:21:03 (Show Source): You can put this solution on YOUR website!let number be x 2x+6 ( 6 plus twice the number) x-7 = (7 less than the number) 2x+6=x-7 2x-x=-7-6 x=-13
 Linear-systems/504388: 2x+4y+16=0 I need this equation in slope-intercept form1 solutions Answer 339581 by mananth(12270)   on 2011-09-25 23:17:56 (Show Source): You can put this solution on YOUR website!slope intercept form equation is y = mx+b 2x+4y+16=0 4y=-2x-16 /4 y=(-1/2)x-4
 Money_Word_Problems/504296: how much money should be invested in an account that earns 9% interest, compounded monthly, if you want to have 5000000 after 20 years1 solutions Answer 339561 by mananth(12270)   on 2011-09-25 21:26:23 (Show Source): You can put this solution on YOUR website!Principal P = x Amount= 5000000 years=n 20 compounded 12 times a year (t) Rate = 9.00 0.750 Amount = P*((n+r)/n)^nt 5000000 = x *( 1 + r/n )^ n 5000000 =P(1+0.090/12)^ 12* 20 5000000 = P( 1.00750 )^ 240 5000000 /( 1.01 )^ 240 = P P= 832064.22
 Travel_Word_Problems/504291: Train a and b are traveling in the same direction on parallel tracks. Train a is traveling at 80 miles per hour and train b is traveling at 90 miles per hour. Train a passes a station at 10:25am. If train b passes the same station at 10:55am, at what time will train b catch up to train a?1 solutions Answer 339558 by mananth(12270)   on 2011-09-25 20:55:37 (Show Source): You can put this solution on YOUR website!Train A 80 mph Train B 90 mph Train A 10:25 Train B 10:55 Difference in time= 00:30 => 0.5 hours Train A will have covered 40 miles before Train B starts from station catch up distance= 40 miles catch up speed = 90 -80 mph catch up speed = 10 mph Catchup time = catchup distance/catch up speed catch up time= 40 / 10 catch up time= 4 hours it will catch up at 2:55 pm
 Travel_Word_Problems/504284: Fran is riding her bike on a 30 mile route. First she rides at a rate of 15 miles per hour. Then she rides at a rate of 6 miles per hour. Her total time is 2.5 hours. Find her distance ridden at 15 miles per hour and her distance ridden at 6 miles per hour1 solutions Answer 339556 by mananth(12270)   on 2011-09-25 20:50:12 (Show Source): You can put this solution on YOUR website!let her ride x miles @ 15mph then she will ride 30-x @ 6mph ... Time at 15 mph + time at 6 mph = total time t=d/r x/15 + (30-x)/6 = 2.5 LCD =30, Multiply by LCD 2x+5(30-x)=2.5*30 2x+150-5x=75 -3x=-75 x=25 25 miles @15 mph 5 miles @6 mph
 Linear-systems/504265: solve and check x/2+x/3=5 how do i find x??1 solutions Answer 339554 by mananth(12270)   on 2011-09-25 20:42:48 (Show Source): You can put this solution on YOUR website! LCD = 6 multiply by the LCD 3x+2x=30 5x=30 x=6 6/2 +6/3 =5
 Mixture_Word_Problems/503758: Corn Syrup worth P44.80 a gallon and maple syrup worth P336 a gallon are mixed to form a mixture worth P132.16 a gallon. How many gallons of each kind of syrup are needed to make 50 gallons of the mixture?1 solutions Answer 339411 by mananth(12270)   on 2011-09-25 03:44:52 (Show Source): You can put this solution on YOUR website!---------price ---------------- quantity corn syrup 44.8 ---------------- x gallons maple syrup 336 ---------------- 50 - x gallons Mixture 132.16% ---------------- 50 44.8 x + 336 ( 50 - x ) = 132.16 * 50 44.8x + 16800 - 336 x = 6608 44.8 x - 336 x = 6608 - 16800 -291.2 x = -10192 / -291.2 x = 35 gallons corn syrup 15 gallons maple syrup
 Travel_Word_Problems/503766: what is the average speed of a car which traveled in a distance of 295 km in 5 hours?1 solutions Answer 339409 by mananth(12270)   on 2011-09-25 03:20:34 (Show Source): You can put this solution on YOUR website!Speed = distance /time Speed =295/5 speed = 59 km/h
 Money_Word_Problems/503729: in order to have \$10,000 in 5 years, how much would a person have to invest if the money will earn 12% interest compounded semiannually?1 solutions Answer 339408 by mananth(12270)   on 2011-09-25 03:18:26 (Show Source): You can put this solution on YOUR website!Principal P = x Amount= 10000 years=n 5 compounded 2 times a year Rate = 12.00 6.000 Amount = P*((n+r)/n)^n 10000 = x *( 1 + r/n )^ n 10000 = P ( 1 + 0.060 / 2 ) ^ 2 * 5 10000 = P( 1.06000 )^ 10 10000 /( 1.06 )^ 10 = P P= 5583.95
 Travel_Word_Problems/503745: two trucks are travel towards each other from points 1,ooo km apart. The two trucks meet each other in 8 hours. What is the average speed of each truck if one truck travels 15 kilometersper hour faster than other? S=d/t1 solutions Answer 339406 by mananth(12270)   on 2011-09-25 02:34:10 (Show Source): You can put this solution on YOUR website!Truck I x km/h Truck II x+ 15 .. They are moving towards each other They are moving towards each other So add up their speed. combined speed = x+ 1 x + 15 ( 2 x + 15 ) Time = 8 hours Distance = 1000 miles Distance = speed * time ( 2 x 15 )* 8 = 1000 16 x + 120 = 1000 16 x = 1000 + -120 16 x = 880 / 16 x= 55 mph Truck I Truck II 55 + 15 = 70 mph
 Numbers_Word_Problems/503362: the smaller of two consecutive odd numbers is n ; the sum of the larger and twice the smaller is 23, find the consecutive numbers1 solutions Answer 339209 by mananth(12270)   on 2011-09-24 04:58:21 (Show Source): You can put this solution on YOUR website!n, n+2 n+2 + 2n = 23 3n+2=23 3n=23-2 3n=21 /3 n=7 7,9
 Rate-of-work-word-problems/503371: The ratio of monthly income to the savings of a family is 11:2 if the savings be Rs. 2500 find the income and expenditure. (Ans. Income Rs. 13750 and Expenditure Rs. 11250)1 solutions Answer 339208 by mananth(12270)   on 2011-09-24 04:55:43 (Show Source): You can put this solution on YOUR website!Income/savings = 11/2 Income / 2500 = 11/2 Income = 2500*11/2 Income = 1250*11 Income = 13750 Income- savings = expenditure
 Percentage-and-ratio-word-problems/503319: Miss Lee distributed some stickers equally among 15 boys and 7 girls. Each boy gave 3/5 of his share to all the girls. As a result, the girls had a total of 768 stickers. What was the total number of stickers Miss Lee had at first?1 solutions Answer 339205 by mananth(12270)   on 2011-09-24 03:27:11 (Show Source): You can put this solution on YOUR website!she had x stickers total 22 kids each got x/22 15 boys they gave 3/5 of x/22 to the girls So they gave a total of 15* 3x/110 = 45x/110 stickers to the girls 7 girls - they have a total of 7*(x/22)=>7x/22 Boys gave 45x/110 7x/22 + 45x/110 = 768 LCD = 110 35x+45x= 110*768 80x=110*768 x=110*768/80 x= 1056 stickers
 Linear-equations/503312: x + 4y = -10 2x – 3y = 13 1 solutions Answer 339202 by mananth(12270)   on 2011-09-24 03:18:14 (Show Source): You can put this solution on YOUR website!1 x + 4 y = -10 .............1 2 x -3 y = 13 .............2 Eliminate y multiply (1)by 3 Multiply (2) by 4 3 x 12 y = -30 8 x -12 y = 52 Add the two equations 11 x = 22 / 11 x = 2 plug value of x in (1) 1 x + 4 y = -10 2 + 4 y = -10 4 y = -10 -2 4 y = -12 y = -3 (2,3) is the solution
 test/503363: Two cell phone companies are advertising rates. Company A charges a rate \$20 per month plus \$0.05 per minute. Company B charges a rate of \$10 per month plus \$0.10 per minute. What is the number of minutes used above which Company A costs more than Company B?1 solutions Answer 339201 by mananth(12270)   on 2011-09-24 03:15:03 (Show Source): You can put this solution on YOUR website!Let x be the number of calls company B 10 + 0.10 x company A 20 + 0.05 x company B < company A 20 + 0.05 x < 10 + 0.10 x 20 + 0.05 x < 10 + 0.10 x 20 - 10 < 0.1 x -0.05 x 10 < 0.05 x 200 < x x should be greater than 200 calls
 Graphs/503318: please help. solve the system below graphically. indicate method you use to plot the lines. show all your wouk. x = 2y 2x + y = -5 b. check by substituting the answer back into the original equations. thank you1 solutions Answer 339200 by mananth(12270)   on 2011-09-24 03:09:29 (Show Source): You can put this solution on YOUR website!x = 2y---------------1 2x + y = -5------------2 equation1 when x= 0 y= 0 ( 0 , 0 ) when y = 0 x= 0 ( 0 , 0 ) Equation 2 when x= 0 y= -5 ( 0 , -5 ) -5 when y = 0 x= -2.5 ( -2.5 , 0 ) The solution is (-2,-1) x=2y -2=-1*2 -2=-2 ... 2x+y=5 2*-2+(-1)*1=-5 -5=-5
 Graphs/503321: please help. solve the following systems of equations using substitution to eliminate one variable. if the system has no solution, indicate that it is inconsistent; if it has infinite solutions, indicate that it is dependant; if the system has one solution, check your answer. y + 5x = 17 4x -3y = 61 solutions Answer 339199 by mananth(12270)   on 2011-09-24 02:32:33 (Show Source): You can put this solution on YOUR website!5 x + 1 y = 17 .............1 -3 y = 6 -4 x ---------2 / -3 = y = -2 + 1.33 x Substitute y in (1) 5 x + 1 ( -2 + 1.33 x ) = 17 5 x -2 + 1.33 x = 17 5 x + 1.33 x = 17 2 6.33 x = 19 / 6.33 x= 3 Plug the value of x in (1) 5 x + 1 y = 17 5 * 3 + 1 y = 17 15 + 1 y = 17 1 y = 2 / 1 y= 2 m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/503346: Two airplanes leave Boston at the same time and fly in opposite directions. If one travels at 420 miles per hour and the other at 440 miles per hour, how long will it take for them to be 3,440 miles apart?1 solutions Answer 339197 by mananth(12270)   on 2011-09-24 02:23:35 (Show Source): You can put this solution on YOUR website!Plane I 420 m/h Plane II 440 m/h Distance 3440 miles Let time they take to be 3440 miles be x hours Plane I distance traveled 420 x miles Plane II distance traveled 440 x miles Time is same t=d/r combined speed= 860 mph 860 x = 3440 x= 4 hours
 Geometry_Word_Problems/503345: A total of \$3900 was invested, part of it at 8% interest and the remainder at 13%. If the total yearly interest amounted to \$395, how much was invested at each rate?1 solutions Answer 339195 by mananth(12270)   on 2011-09-24 02:12:21 (Show Source): You can put this solution on YOUR website!Investment I 8.00% per annum ---x Investment II 13.00% per annum ---y x + y= 3900 ------------------------1 8.00% x + 13.00% y = \$395.00 Multiply by 100 8 x + 13 y = \$39,500.00 Multiply (1) by -8 we get -8 x -8 y = -31200.00 Add this to (2) 0 x +5 y = \$8,300.00 divide by 5 y = \$1,660.00 Balance \$2,240.00 CHECK \$2,240.00 --------- 8.00% ------- \$179.20 \$1,660.00 ------- 13.00% ------- \$215.80 Total ------- \$395.00
 Mixture_Word_Problems/503347: Suppose that a pharmacist has a supply of a 30% solution of alcohol and a 70% solution of alcohol. How many quarts of each should be mixed to produce 60 quarts that is 50% alcohol? thank you1 solutions Answer 339194 by mananth(12270)   on 2011-09-24 02:07:02 (Show Source): You can put this solution on YOUR website!---------percent ---------percent ---------------- quantity Alcohol I 30 ---------------- x quarts Alcohol II 70 ---------------- 60 - x quarts Mixture 50.00% ---------------- 60 30 x + 70 ( 60 - x ) = 50 * 60 30x+4200-70x=3000 30x-70x =3000 -4200 -40 x = -1200 / -40 x = 30 quarts 30.00% Alcohol I 30 quarts 70.00% Alcohol II
 test/503352: A fitness club requires a \$100 initiation fee and dues of \$25 each month.write an expression for the cost of membership for n months.t hen find the cost of membership for one year 1 solutions Answer 339193 by mananth(12270)   on 2011-09-24 02:02:26 (Show Source): You can put this solution on YOUR website!Down payment = \$100 per month = \$25 number of months = n C(m)= 100+25n For 1 year = 12 months C(m)=100+25*12 C(m)=400
 Mixture_Word_Problems/503241: Two bank loans, one for \$5000 and the other for \$3000, cost a toatl of\$550 in interest for one year. The \$5000 loan has an interest rate 3% lower than the interest rate for the \$3000 loan. Find the interest rate for each loan.1 solutions Answer 339179 by mananth(12270)   on 2011-09-23 21:07:18 (Show Source): You can put this solution on YOUR website!\$3,000.00 --------- x% \$5,000.00 -------- x% -3.00% \$3,000.00*x%+\$5,000.00(x-3.00%)=550 30 x+ 50 x -150.00 = 550 80 x = 700 x= 8.75 % on \$3000 5.75% on \$5000