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# Recent problems solved by 'mananth'

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 Travel_Word_Problems/633034: An airplane leaves los angeles for Denver at a speed of 450 mph.Thirty min later,a plane going from Denver yo los Angeles leaves Denver,which is 850 miles from los Angeles,at a speed of 520 mph.When they meet, how far are they from Denver?1 solutions Answer 398615 by mananth(12270)   on 2012-07-29 23:35:23 (Show Source): You can put this solution on YOUR website!Let them meet at distance x from Denver LA to Denver - speed = 450 mph Denver to LA = 520 mph ( 30 minutes later) Total distance = 850 miles d=rt When the second plane starts the first plane has already traveled 450*1/2 = 225 miles so the distance between them will be 625 miles add up their speeds = 520+450 = 970 mph time = d/r time = 625/970 = 0.64 hours Distance from denver = 0.64*520= 334.8 miles m.ananth@hotmail.ca
 Travel_Word_Problems/633037: At 14 miles per hour how many feet does a car travel in a minute?1 solutions Answer 398611 by mananth(12270)   on 2012-07-29 23:24:18 (Show Source): You can put this solution on YOUR website!14 mph 1 mile = 5280 feet 1 hour = 60 minutes 14 mph = 14*5280/60= 1232feet/minute
 Age_Word_Problems/633036: The age of the father of two children is twice that of the elder one added to four times that of the younger one. If the geometric mean of the ages of the two children is 4√3 and their harmonic mean is 6, then what is the father's age?1 solutions Answer 398610 by mananth(12270)   on 2012-07-29 23:21:18 (Show Source): You can put this solution on YOUR website!Let the childrens' age be x & y , x >y Father's age 2x+4y xy= 48 Harmonic mean =6 xy = 48 = 6 x+y = 16 xy = 48 x=48/y multiply equation by y (y-8)(y-6)=0 y= 8 OR 6 xy = 48 therefore x=8 The sons' ages are 8 & 6 Father's age 2x+4y -> 2*8+4*6 =40 years m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/633002: A boat traveled for 3 hr with a 12-mph current to reach a picnic area. The return trip against the same current took 12 hr. Find the speed of the boat in still water. 1 solutions Answer 398608 by mananth(12270)   on 2012-07-29 22:58:50 (Show Source): You can put this solution on YOUR website!Boat speed x mph current speed 12 mph .. against currentspeed x- 12 withcurrent x+ 12 .. Against current 12 hours with current x+y 3 hours Distance is same. D=r*t 12(x-12)=3(x+12 ) 12x-144 =3x+36 12x-3x =144+36 9x=180 / 9 x= 20 mph Boat speed = 20 mph
 Miscellaneous_Word_Problems/633003: A plane flies 500 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 30 mph, what is the speed of the plane in still air?1 solutions Answer 398606 by mananth(12270)   on 2012-07-29 22:47:03 (Show Source): You can put this solution on YOUR website!Plane speed x mph wind speed 30 mph .. against wind x - 30 mph with wind x + 30 mph Distance against wind 350 Distance with wind 500 Time = same equate the time against with time with current t=d/r 350 /(x- 30 )= 500 /(x+ 30 ) 350 *(x+ 30 )= 500 *(x- 30 ) 350 x + 10500 = 500 x -15000 350 x -500 x = -15000 + -10500 -150 x = -25500 / -150 x= 170 mph ---- Plane speed m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/633023: Factor(25x^2-4/49) Would you please show the steps that derive the solution below? Microsoft Mathmatics solution is 1/49(35x-2)(35x+2)1 solutions Answer 398604 by mananth(12270)   on 2012-07-29 22:40:26 (Show Source): You can put this solution on YOUR website! applyig the identity LCD = 7 m.ananth@hotmail.ca
 Linear-equations/632836: Please find the slope-intercept and standard form of this equation: m= -3 P1 = (-2, -3) 1 solutions Answer 398515 by mananth(12270)   on 2012-07-29 08:54:39 (Show Source): You can put this solution on YOUR website!m= -3 Plug value of the slope and point ( -2 , -3 ) in y=mx+b -3.00 = -3 * -2 +b b= -3 + -6 b= -9 So the equation will be Y = -3 x -9 (slope intercept form) 3x+y =9 m.ananth@hotmail.ca
 Evaluation_Word_Problems/632735: solve using the elimination method. show your work. if the system has no solution or an infinite number of solutions, state this. -12x+27y=60 -6x-6y=301 solutions Answer 398509 by mananth(12270)   on 2012-07-29 06:12:46 (Show Source): You can put this solution on YOUR website!-12 x + 27 y = 60.00 .............1 -6x-6y=30 /6 -1 x -1 y = 5.00 .............2 Eliminate y multiply (1)by 1 Multiply (2) by -27 -12 x 27 y = 60.00 27 x + 27 y = -135.00 Add the two equations 15 x = -75.00 / 15 x = -5.00 plug value of x in (1) -12 x + 27 y = 60 60 + 27 y = 60 27 y = 60 -60 27 y = 0 y = 0.00 x=-5,y=0
 Money_Word_Problems/632773: a woman has some stocks that yield 5% annually and some bonds that yield 10%. If her investment totals \$6000 and her annual income from the investment is \$400, how much does she have invested in stocks and how much in bonds?1 solutions Answer 398506 by mananth(12270)   on 2012-07-29 06:06:33 (Show Source): You can put this solution on YOUR website!Stocks 5.00% per annum ------------- Amount invested =x Bonds 10.00% per annum ------------ Amount invested = y 6000 Interest----- 400 Stocks 5.00% per annum ---x Bonds 10.00% per annum ---y Credit on both cards x + 1 y= 6000 -------------1 Interestto be paid on both 5.00% x + 10.00% y= 400 Multiply by 100 5 x + 10 y= 40000.00 --------2 Multiply (1) by -5 we get -5 x -5 y= -30000.00 Add this to (2) 0 x 5 y= 10000 divide by 5 y = 2000 Stocks 5.00% \$ 4000 Bonds 10.00% \$ 2000 CHECK 4000 --------- 5.00% ------- 200.00 2000 ------------- 10.00% ------- 200.00 Total -------------------- 400.00 m.ananth@hotmail.ca
 Angles/632831: find the measure of an angle whose supplement is 45 degrees less than 4 times its complement.1 solutions Answer 398505 by mananth(12270)   on 2012-07-29 06:02:28 (Show Source): You can put this solution on YOUR website!Let the angle be x supplement of angle = 180-x Complement of angle = 90-x 4 times= 4(90-x) 4(90-x)-(180-x)=45 360-4x-180+x=45 135=3x /3 x= 45 measure of angle = 45 deg
 Money_Word_Problems/632829: A woman has some stocks that yield 5% annually and some bonds that yield 10%. If her investment totals \$6,000 and her annual income from the investments is \$400, how much does she have invested in stocks and how much in bonds ? 1 solutions Answer 398504 by mananth(12270)   on 2012-07-29 05:59:22 (Show Source): You can put this solution on YOUR website!Stocks 5.00% per annum ------------- Amount invested =x Bonds 10.00% per annum ------------ Amount invested = y 6000 Interest----- 400 Stocks 5.00% per annum ---x Bonds 10.00% per annum ---y Credit on both cards x + 1 y= 6000 -------------1 Interestto be paid on both 5.00% x + 10.00% y= 400 Multiply by 100 5 x + 10 y= 40000.00 --------2 Multiply (1) by -5 we get -5 x -5 y= -30000.00 Add this to (2) 0 x 5 y= 10000 divide by 5 y = 2000 Stocks 5.00% \$ 4000 Bonds 10.00% \$ 2000 CHECK 4000 --------- 5.00% ------- 200.00 2000 ------------- 10.00% ------- 200.00 Total -------------------- 400.00 m.ananth@hotmail.ca
 Linear-equations/632830: 5y-5x=3(x+y-1) please transform in standard form1 solutions Answer 398503 by mananth(12270)   on 2012-07-29 05:57:29 (Show Source): You can put this solution on YOUR website!5y-5x=3(x+y-1) 5y-5x=3x+3y-3 5y-3y-5x-3x=-3 2y-8x=-3 8x-2y=3
 Mixture_Word_Problems/632780: The cost of 8 adult's tickets and 7 children's tickets is \$82.45. The cost of 4 adult's tickets and 9 children's tickets is \$65.15. Find the cost of each adult's ticket and each child's ticket. In the answer box below enter the cost of each adult's ticket 1 solutions Answer 398502 by mananth(12270)   on 2012-07-29 05:55:34 (Show Source): You can put this solution on YOUR website!x Adult Ticket y Chuild Ticket Total tickets 8 x + 7 y = 82.45 .............1 4 x + 9 y = 65.15 .............2 Eliminate y multiply (1)by 9 Multiply (2) by -7 72 x 63 y = 742.05 -28 x -63 y = -456.05 Add the two equations 44 x = 286.00 / 44 x = 6.50 plug value of x in (1) 8 x + 7 y = 82 52 + 7 y = 82 7 y = 82 -52 7 y = 30 y = 4.35 Adult Ticket \$ 6.50 Child ticket \$4.35
 Money_Word_Problems/632828: Dorothy owes \$11,000 on two credit cards with annual interest rates 9% and 12 %. If she pays \$1,140 in interestfor the year, how much does she owe on each card ? 1 solutions Answer 398501 by mananth(12270)   on 2012-07-29 05:47:27 (Show Source): You can put this solution on YOUR website!Card I 9.00% per annum ------------- Amount invested =x Card II 12.00% per annum ------------ Amount invested = y 11000 Interest----- 1140 Card I 9.00% per annum ---x Card II 12.00% per annum ---y Credit on both cards x + 1 y= 11000 -------------1 Interestto be paid on both 9.00% x + 12.00% y= 1140 Multiply by 100 9 x + 12 y= 114000.00 --------2 Multiply (1) by -9 we get -9 x -9 y= -99000.00 Add this to (2) 0 x 3 y= 15000 divide by 3 y = 5000 Card I 9.00% \$ 6000 Card II 12.00% \$ 5000 CHECK 6000 --------- 9.00% ------- 540.00 5000 ------------- 12.00% ------- 600.00 Total -------------------- 1140.00 m.ananth@hotmail.ca
 Money_Word_Problems/632787: dorothy owes \$11000 on two credit cards with annual interest rates of 9% and 12%. If she pays \$1140 interest for the year, how much does she owe on each card?1 solutions Answer 398500 by mananth(12270)   on 2012-07-29 05:46:49 (Show Source): You can put this solution on YOUR website!Card I 9.00% per annum ------------- Amount invested =x Card II 12.00% per annum ------------ Amount invested = y 11000 Interest----- 1140 Card I 9.00% per annum ---x Card II 12.00% per annum ---y Credit on both cards x + 1 y= 11000 -------------1 Interestto be paid on both 9.00% x + 12.00% y= 1140 Multiply by 100 9 x + 12 y= 114000.00 --------2 Multiply (1) by -9 we get -9 x -9 y= -99000.00 Add this to (2) 0 x 3 y= 15000 divide by 3 y = 5000 Card I 9.00% \$ 6000 Card II 12.00% \$ 5000 CHECK 6000 --------- 9.00% ------- 540.00 5000 ------------- 12.00% ------- 600.00 Total -------------------- 1140.00 m.ananth@hotmail.ca
 Mixture_Word_Problems/632793: How many ounces of a 50 % acetic acid solution should a photographer add to 32 ounces of a 5 % solution to obtain 30 % acetic acid1 solutions Answer 398499 by mananth(12270)   on 2012-07-29 05:40:23 (Show Source): You can put this solution on YOUR website!-------------- percent ---------------- Amount Acetic acid I 5 ---------------- 32 Ounces Acetic acid II 50 ---------------- x Ounces Mixture 30 ---------------- 32 + x Ounces 5*32+50 x =30(32+x) 160+50x =960+30x 50x-30x =-160+ 960 20x=800 / 20 x = 40 Ounces Acetic acid II m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/632798: I don't understand how to write x^10-1 as a product of two terms?1 solutions Answer 398498 by mananth(12270)   on 2012-07-29 05:37:19 (Show Source): You can put this solution on YOUR website!The identity
 Linear-systems/632251: i need help on elimination method please help me to solve this equation 5x-2y=3 2x+5y=41 solutions Answer 398202 by mananth(12270)   on 2012-07-27 02:25:08 (Show Source): You can put this solution on YOUR website!5 x -2 y = 3 .............1 2 x + 5 y = 4 .............2 Eliminate y multiply (1)by 5 Multiply (2) by 2 25 x -10 y = 15 4 x + 10 y = 8 Add the two equations 29 x = 23 / 29 x = 4/5 plug value of x in (1) 5 x -2 y = 3 4 -2 y = 3 -2 y = 3 -4 -2 y = -1 y = 1/2 x=4/5, y= 1/2
 Travel_Word_Problems/632285: Karen traveled 640 miles by boat and returned by plane. She spent 42 hours traveling on the trip. If the rate of the plane is 20 times faster than the rate of the boat, find each rate.1 solutions Answer 398201 by mananth(12270)   on 2012-07-27 02:21:49 (Show Source): You can put this solution on YOUR website!let boat speed = x mph plane speed = 20 x Time forward + time return = 42 hours distance one way = 640 miles time = d/r 640/x + 640/20x= 42 LCD = 20x (640*20 +640)/20x= 42 12800 +640= 42*20x 13440= 840x x= 13440/840 x= 16 mph the speed of boat speed of plane = 16*20 = 320 mph m.ananth@hotmail.ca
 Travel_Word_Problems/632288: Two crews working toward each other are 21.25 miles apart. One crew paves 1.4 miles of highway per day, and the other paves 1.1 miles per day. How long will it take them to meet? Give the answer to one decimal place, if necessary.1 solutions Answer 398199 by mananth(12270)   on 2012-07-27 02:16:25 (Show Source): You can put this solution on YOUR website!Crew I -------- 1.4 miles per day Crew II -------- 1.1 miles per day they are paving towards each other so add up rate of work 1.4 + 1.1 = 2.5 miles per day Distance = 21.25 miles time = d/r time= 21.25 / 2.5 Time = 8.5 days
 Travel_Word_Problems/632320: During the first part of a trip, a canoeist travels 42 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 4 hrs. What was the speed on each part of the trip?1 solutions Answer 398198 by mananth(12270)   on 2012-07-27 02:12:03 (Show Source): You can put this solution on YOUR website!First Part 42 miles Second Part 4 miles First Part x mph Second Part x -5 mph Total time 4 hours First Part time 42 / x Second Part time 4 / ( x -5 ) Time first part + time second part = 4 hours 42 / x + 4 /(x -5 ) = 4 LCD = ( x + 0 )* (x -5 ) multiply the equation by the LCD we get 42 * (x+ -5 )+ 4 x = 4 42 x+ -210 + 4 x = 4 X^2 -20 x 66 x+ -210 = 4 X^2 4 X^2 -66 x+ 210 = 0 4 X^2+ -66 x+ 210 = = 0 / 4 4 X^2 -66 x+ 210 = 0 Find the roots of the equation by quadratic formula a= 4 b= -66 c= 210 b^2-4ac= 4356 - 3360 b^2-4ac= 996 = 31.56 OK 5 x1=( 66 + 31.56 )/ 8 x1= 12.19 x2=( 66 -31.56 ) / 8 x2= 4.31 x2 is not possible so x= 12.2 mph first part of trip 7.2 mph second part of trip. (12.2-5) m.ananth@hotmail.ca
 Geometry_Word_Problems/632322: The side of a square has length s . The length of a rectangle is 4 m more than the side of the square and the width of the rectangle is 2 m less than the side of the square. The perimeter of the rectangle is 24 m less than twice the perimeter of the square. Find the dimensions of each figure.1 solutions Answer 398196 by mananth(12270)   on 2012-07-27 01:57:29 (Show Source): You can put this solution on YOUR website!Perimeter of square = 4s twice perimeter of square = 4s*2 = 8s Length of rectangle = s+4 Width of rectangle = s-2 Perimeter = 2(l+w) Perimeter = 2(s+4+s-2) =2(2s+2) =4s+4 8s-(4s+4) =24 8s-4s-4=24 4s-4=24 4s=28 s=7 side of square = 7m Length of lectangle = 7+4=11m width of rectangle = 7-2=5m
 Quadratic_Equations/632318: Solve for x. 2(x-4)-(x+2)=(x+2)(x-4)1 solutions Answer 398195 by mananth(12270)   on 2012-07-27 01:51:34 (Show Source): You can put this solution on YOUR website!2(x-4)-(x+2)=(x+2)(x-4) simplify (x-1)(x-2)=0 so x= 1 OR 2 -
 Travel_Word_Problems/632293: Granville and Preston are 528 miles apart. A car leaves Preston bound for Granville at 47 mph. At the same time, another car leaves Granville bound for Preston at 41 mph. How long will it take them to meet?1 solutions Answer 398192 by mananth(12270)   on 2012-07-27 01:33:31 (Show Source): You can put this solution on YOUR website!Granville bound -------- 47 mph Preston bound -------- 41 mph they are traveling towards each other so add up speeds 47 + 41 = 88 km/h Distance = 528 km time = d/r time= 528 / 88 Time = 6 h They will meet after 6 hours
 Mixture_Word_Problems/632314: How many gallons of 60% antifreeze solution must be mixed with 100 gallons of 20% antifreeze to get a mixture that is 50% antifreeze? Use the six-step method.1 solutions Answer 398190 by mananth(12270)   on 2012-07-27 01:27:04 (Show Source): You can put this solution on YOUR website!-------------- percent ---------------- Amount Antifreeze I 20 ---------------- 100 gal Antifreeze II 60 ---------------- x gal Mixture 50 ---------------- 100 + x gal 20 * 100 + 60 x = 50 ( 100 + x ) 2000 + 60 x = 5000 + 50 x 60 x -50 x = -2000 + 5000 10 x = 3000 / 10 x = 300 gal Antifreeze II m.ananth@hotmail.ca
 Money_Word_Problems/632315: Nico is saving money for his college education. He invests some money at 8%, and \$1200 less than that amount at 5%. The investments produced a total of \$174 interest in 1 year. How much did he invest at each rate?1 solutions Answer 398189 by mananth(12270)   on 2012-07-27 01:24:58 (Show Source): You can put this solution on YOUR website!8%--------------- x 5% x-1200 Interest = 174 8%x+(x-1200)*5%= 174 multiply equation by 100 8x+5(x-1200)= 17400 8x+5x-6000=17400 13x= 17400+6000 13x= 23400 x=1800 Investment @ 8% = \$1800 Investment at 5% = 1800-1200 = 600
 Linear-equations/632316: find the equation of the line passing (0,1) parallel to the line 2x-3y=61 solutions Answer 398187 by mananth(12270)   on 2012-07-27 01:15:54 (Show Source): You can put this solution on YOUR website!2 x -3 y = 6 Find the slope of this line make y the subject -3 y = -2 x + 6 Divide by -3 y = 2/3 x -2 Compare this equation with y=mx+b slope m = 2/3 The slope of a line parallel to the above line will be the same The slope of the required line will be 2/3 m= 2/3 ,point ( 0 , 1 ) Find b by plugging the values of m & the point in y=mx+b 1 = 0 + b b= 1 m= 2/3 Plug value of the slope and b in y = mx +b The required equation is y = 2/3 x + 1 m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/632295: What are the steps to sovling questions like x to the second power = 49 or x2=491 solutions Answer 398186 by mananth(12270)   on 2012-07-27 01:14:14 (Show Source): You can put this solution on YOUR website! take the square root on both sides x= +/- 7
 Linear_Equations_And_Systems_Word_Problems/631663: the perimeter of a rectangle is 80m.the length is decresed by 2m and width is increased by 2m.By doing this the area of a rectangle will be increased by 36 sq.m. What is the length and width?1 solutions Answer 397733 by mananth(12270)   on 2012-07-25 02:06:05 (Show Source): You can put this solution on YOUR website!let length be l & width be w 2(l+w)= 80 perimeter l+w = 40 new length = (l-2) new width = (w+2) New area - old area = 36 (l-2)(w+2)-lw=36 lw+2l-2w-4-lw=36 2l-2w=40 /2 l-w=20 l+w=40 add both equations 2l=60 l=30 so w=10 The dimensions of rectangle are 30 & 10 m
 Travel_Word_Problems/631659: A motorboat can maintain a constant speed of 16 mph relative to the water. The boat makes a trip upstream to a marina in 20 minutes. The return trip takes 15 minutes. What is the speed of the current? 1 solutions Answer 397730 by mananth(12270)   on 2012-07-25 01:19:08 (Show Source): You can put this solution on YOUR website!Let current speed = x mph upstream speed = 16-x mph downstream speed= 16+x mph Time upstream = 1/3 hours Time downstream = 1/4 hours Distance upstream = distance downstream distance = speed * time 1/3(16-x) = 1/4(16+x) multiply equation by LCD 12 4(16-x)=3(16+x) 64-4x = 48+3x 64-48= 7x 16=7x x= 16/7 x= 2.3 mph the current speed
 Expressions-with-variables/631622: I need some guidance on this word problem please. I need to find how a population grows over seven months. r: remains constant. For the first month I have 10 rabbits and end with 15, which is a larger number that depends on r ( the intrinsic rate of growth). The beginning of the second time step starts with the number at the end of the previous step. Round to the nearest whole number.At the end of 7 months, how large did the population become? Thank you , Ann 1 solutions Answer 397717 by mananth(12270)   on 2012-07-24 23:22:02 (Show Source): You can put this solution on YOUR website!This is and arithmetic progression Starting a= 10 next month it is 15 so the difference d = 5 the number of months = n = 7 Apply the formula Tn=a+(n-1)d where Tn is the nth. term T7 = 10 +(7-1)*5 T7 = 10+30 T7 = 40 Population at the end of 7 months = 40 m.ananth@hotmail.ca