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# Recent problems solved by 'mananth'

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 Age_Word_Problems/323957: Mary is presently twice as old as Maggy. Ten years ago, Maggy's age was one-third of Mary's then. Ten years from now, Maggy's age will be three-fifths of Mary's age then. How old is each?1 solutions Answer 231875 by mananth(12270)   on 2010-07-20 10:33:53 (Show Source): You can put this solution on YOUR website!Let Maggy's age = x Mary's age = 2x .. ten years later their ages will be Maggie= x+10 Mary = 2x+10 .. x+10 = 3/5 (2x+10) 5(x+10)=3(2x+10) 5x+50=6x+30 6x-5x=50-30 x=20 years Maggie's age Mary's age = 2x = 40 years
 logarithm/323979: Solve: 27x + 2 = 81-2 + x 1 solutions Answer 231873 by mananth(12270)   on 2010-07-20 10:28:00 (Show Source): You can put this solution on YOUR website!27x + 2 = 81-2 + x add =2 to both sides 27x+2-2=81-2-2+x 27x=77+x add -x to both sides 27x-x=77+x-x 26x=77 divide by 26 x=77/26
 test/323986: The shortest leg of a right triangle is 2 less than the hypotenuse and the hypotenuse is one longer than the longest leg right in quadratic equation form 1 solutions Answer 231869 by mananth(12270)   on 2010-07-20 10:21:00 (Show Source): You can put this solution on YOUR website!longest leg be x hypotenuse= x+1 shortest leg = x-2 .. x^2+(x-2)^2= (x+1)^2
 Quadratic-relations-and-conic-sections/323978: what is the y-coordinate of the vertwx of the parabola that is given by the equation below? y=1.5(x-2)^2+7 1 solutions Answer 231867 by mananth(12270)   on 2010-07-20 10:15:44 (Show Source): You can put this solution on YOUR website!(h,k )are the co-ordinates of the parabola y^2= a(h-k)^2+k This is in the vertex form so the co-ordinates of vertex are (2,7)
 Equations/323975: Which quadratic equation has roots 7 and -2/3? a) 2x^2 - 11x - 21=0 b) 3x^2 - 19x - 14=0 c) 3x^2 + 23x + 14=0 d) 2x^2 + 11x - 21=01 solutions Answer 231856 by mananth(12270)   on 2010-07-20 09:34:55 (Show Source): You can put this solution on YOUR website! The roots are 7 & -2/3 So the factors are (x-7)(3x+2) 3x^2+2x-21x-14 3x^2-19x-14
 Miscellaneous_Word_Problems/323966: A certain cake recipe states that the cake should be baked in a pan 8 inches in diameter. if jules wants to use the recipe to make a cake of the same depth but 12 inches in diameter, by what factor should he multiply the recipe ingredients ? A 2 1/2 B 2 1/4 C 1 1/2 D 1 4/9 E 1 1/3 1 solutions Answer 231848 by mananth(12270)   on 2010-07-20 09:22:50 (Show Source): You can put this solution on YOUR website!you have to compare the ratios of the area OR the ratio of the squares of the radius. 12" dia = 6" radius 8" diameter = 4" radius .. r^2= 36 r^2=16 .. Ratio = 36/16 =2.25 times OPTION B
 Average/323945: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? solution: Speed= 60X5/18 m/sec = 50/3m/sec length of the train = S X D = 50/3 X 9m = 150m when do we use 5/18 ?1 solutions Answer 231825 by mananth(12270)   on 2010-07-20 07:36:13 (Show Source): You can put this solution on YOUR website!1 km/hour = 1000 meters/3600 seconds =5/18 meters / second .. 60 km/hour = 60 *5/18 = 16.66 m/second
 Problems-with-consecutive-odd-even-integers/323942: Factor completely. If a polynomial is prime, state this 15t^2 + 20t- 75 help me with this1 solutions Answer 231824 by mananth(12270)   on 2010-07-20 07:31:05 (Show Source): You can put this solution on YOUR website!15t^2 + 20t- 75 5(3t^2+4t-15) 5(3t^2+9t-5t-15) 5(3t(t+3)-5(t+3)) 5(t+3)(3t-5)
 Problems-with-consecutive-odd-even-integers/323940: using the five-step problem-solving process A rancher outside Houston decides to build a silo inside his corral. The rectangular corral measures 23 m by 17 m and the silo's base is circular with a diameter of x meters. Find a polynomial for the remaining area of the corral (in square meters) after the silo is built. 1 solutions Answer 231823 by mananth(12270)   on 2010-07-20 07:28:09 (Show Source): You can put this solution on YOUR website!Length of corral = 23 m width of corral = 17m .. Area of Corral = 17*23 = 391 m^2 .. diameter of silo = x radius = x/2 .. Area of circle = pi*r^2 Area = pi*(x/2)^2 .. Area of corral - area of silo = area of remaining area 391- pi*(x/2)^2
 test/323938: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?1 solutions Answer 231822 by mananth(12270)   on 2010-07-20 07:23:00 (Show Source): You can put this solution on YOUR website!60 km/hour = 60*1000 meters/ 3600 seconds = 16.6 meters/second .. speed = 16.6 meters/second time = 9 seconds distance traveled = length of the train 16.6 *9= 149.5 meters
 Age_Word_Problems/323937: grace is four times as old as vicky. five yrs ago, vicky was thirty yrs younger than grace. find their ages.1 solutions Answer 231821 by mananth(12270)   on 2010-07-20 07:14:49 (Show Source): You can put this solution on YOUR website!let vicky's age =x grace = 4x .. 5 years ago their ages were vicky x-5 grace 4x-5 .. 4x-5 -30= x-5 4x-35= x-5 3x=30 x=10 vicky"s age now Grace's age = 40
 Linear-equations/323934: Write the equation of the line which passes through (0, -4) and is parallel to the line 3x - y = 6. 1 solutions Answer 231820 by mananth(12270)   on 2010-07-20 07:10:47 (Show Source): You can put this solution on YOUR website!line equation 3x-y=6 put it in the form y = mx +b y=3x-6 the slope is 3 and b = -6 the line parallel to this will have the same slope. m=3 plug the value (0,-4) in the equation y= mx+b b=-4 y=3x-4 is the line passing through (0,-4)
 Equations/323935: 9-2(7x-5)=3(x-5)1 solutions Answer 231817 by mananth(12270)   on 2010-07-20 06:55:08 (Show Source): You can put this solution on YOUR website!9-2(7x-5)=3(x-5) 9-14x+10=3x-15 -14x+19=3x-15 -17x=-34 x=2
 Graphs/323881: Find the x- and y-intercepts apply elimination or substitution to find the coordinates of the point of intersection. 15x + 11y = -17 8x - 6y = 741 solutions Answer 231812 by mananth(12270)   on 2010-07-20 04:31:50 (Show Source): You can put this solution on YOUR website!15x + 11y = -17................1 8x - 6y = 74...................2 multiply equation 1 by 6 and equation 2 by 11 and add them. to eliminate y .. 90x+66y=-102 88x-66y=814 178x=712 x= 712/178 x= 4 plug the value of x in any equation 90*4 +66y=-102 360+66y=-102 66y=-102-360 66y=-462 y=-7 The intercepts are (4, -7)
 Equations/323891: Ray and Amir each bought a used car for the same price. Each needed repairs. The repairs on Ray's car cost an additional \$800 and on Amir's, \$200. Amir noted, "Ray, my total cost was really only 5/6 of your total cost." How much did each pay for his used car? 1 solutions Answer 231811 by mananth(12270)   on 2010-07-20 04:23:15 (Show Source): You can put this solution on YOUR website!let the price of their cars be \$X Ray cost = x+800 Amir's cost = x+200 x+200= 5/6 ( x+800) 6(x+200)= 5(x+800) 6x+1200 = 5x+4000 x= 4000-1200 x= \$2800 price of car
 Word_Problems_With_Coins/323893: In a collection of coins consisting of only nickels and pennies, the total value is \$1.10 and there are twice as many nickels as pennies. How many nickels are in the collection? 1 solutions Answer 231810 by mananth(12270)   on 2010-07-20 04:13:52 (Show Source): You can put this solution on YOUR website!let pennies be x nickels = 2x x+ 5*2x =110 cents x+10x=110 11x=110 x= 10 pennies nickels = 2x = 20
 Travel_Word_Problems/323903: if you are going 4/10 of a mile how many seconds you would go at 60 miles per hour? 1 solutions Answer 231809 by mananth(12270)   on 2010-07-20 04:05:38 (Show Source): You can put this solution on YOUR website!time = distance / speed d= 4/10 speed = 60mph time = 4/10 / 60 =4/10 * 1/60 =1/150 hours 1/150 * 3600 =24 seconds
 Triangles/323922: The perimeter of a right triangle is 12 ft, and one of its legs measures 3 ft. Find the length of the other leg and the hypotenuse. 1 solutions Answer 231808 by mananth(12270)   on 2010-07-20 04:00:20 (Show Source): You can put this solution on YOUR website!let x be the hypotenuse and y be the other leg one leg = 3 .. x^2-y^2= 9 (x+y)(x-y)=9 (x+y)=9 9(x-y)=9 x-y =1 x+y+3=12 .. Add the 2 equations x-y+x+y+3=12+1 2x+3=13 2x=10 x=5 feet the hypotenuse the second leg will be 4 feet
 Length-and-distance/323902: What is the equation of the line perpendicular to the line joining (4, 2) and (3, -5) and passing through (4, 2)?1 solutions Answer 231807 by mananth(12270)   on 2010-07-20 03:44:16 (Show Source): You can put this solution on YOUR website!(4,2 ) (3, -5) slope of the line joining them is m= y2-y1/x2-x1 m=-5-2 / 3-4 =-7/-1 m=7 so the general equation is y=7x+b plug the value of any one poin to get the value of b 2=28+b b=-26 The line perpendicular to it will have slope o -1/7 The equation for that lineis y= -1/7 x -26
 Mixture_Word_Problems/323909: chandra has 3 liters of a 14% solution of sodium hydroxide in a container. What is the amount and concentration of sodium hydroxide solution she must add to this in order to end up with 7 liters of 34% solution?1 solutions Answer 231806 by mananth(12270)   on 2010-07-20 03:28:03 (Show Source): You can put this solution on YOUR website!chandra has 3 liters of a 14% solution of sodium hydroxide in a container. What is the amount and concentration of sodium hydroxide solution she must add to this in order to end up with 7 liters of 34% solution? 3 liters 14% total is 7 liters so 4 liters x% .. Total 7 liters 34% .. Equation for concentration 3*0.14 +4*0.01x = 7*0.34 0.42+0.04x=2.38 0.04x=2.38-0.42 0.04x= 1.96 x= 49% and 4 liters is to be added
 Polynomials-and-rational-expressions/323921: (4y-8)^2= 16y^2-64y-10 is what i put in(computer online course)but it says it's wrong. I asked this but put in the wrong email address, I'm sorry for my mistake.thank you for help1 solutions Answer 231803 by mananth(12270)   on 2010-07-20 03:14:59 (Show Source): You can put this solution on YOUR website!(4y-8)^2= 16y2-64y+64
 Miscellaneous_Word_Problems/323913: When 358, 528 and 698 are in turn divided by a certain number, the remainder is 1 in each case. Find the number.-1 solutions Answer 231802 by mananth(12270)   on 2010-07-20 02:20:18 (Show Source): You can put this solution on YOUR website!When 358, 528 and 698 are in turn divided by a certain number, the remainder is 1 in each case. Find the number.- .. the difference between the numbers is 170 528-358=170 698-528=170 .. 170= 17*10 !7 is the number
 Miscellaneous_Word_Problems/323915: To lap a running track, Tom takes 65 seconds, Dick takes 70 seconds and Harry takes 75 seconds. If they start together, when will they next be together at the starting point?1 solutions Answer 231800 by mananth(12270)   on 2010-07-20 02:02:17 (Show Source): You can put this solution on YOUR website!In such problems you have to take the LCM of the numbers. That is when they are together Factors of 60= 2*2*3*5 Factors of 70 are 2* 5*7 Factors of 75 are 3*5*5 The LCM will be 2100 After 2100 seconds they will be together after 2100 seconds
 Triangles/323639: The area of a triangle with height 5 inches is equal to the area of a certain rectangle of length 10 inches and width 7 inches. What is the base of the triangle?1 solutions Answer 231596 by mananth(12270)   on 2010-07-19 10:54:05 (Show Source): You can put this solution on YOUR website!length of rectangle = 10 width of rectangle =7 Area = 70 sq.in .. Area of triangle = 1/2 * base * h h = 5 in Area =70 base = area *2 / h base = 70*2/5 =14*2 = 28 inches height
 Human-and-algebraic-language/323635: I have to make an equation for this problem: A teacher goes to Company B to buy supplies and for every dollar amount spent over \$20 there is a 30% discount given. I thought the equation would be y=.30x+20 or y=x-20(.30). Are either of these correct?1 solutions Answer 231595 by mananth(12270)   on 2010-07-19 10:50:10 (Show Source): You can put this solution on YOUR website!let him buy \$x worth material above \$20 So for every dollar he spends above \$20 he pays \$0.7 so for \$x he will pay 0.7x Totally he will pay 20 + 0.7x dollars
 Money_Word_Problems/323543: Of the \$50,000 that Natasha pocketed on her last real estate deal, \$20,000 went to charity. She invested part of the remainder in Dreyfus New Leaders Fund with an annual yield of 16% and the rest in Templeton Growth Fund with an annual yield of 25%. If she made \$6060 on these investments in 1 year, then how much did she invest in each fund?1 solutions Answer 231584 by mananth(12270)   on 2010-07-19 10:17:50 (Show Source): You can put this solution on YOUR website!\$ 50,000 was the amount received. 20000 went to charity So she invested \$30,000 Let her invest x in New Leader - 16% she will invest 30,000-x in Templeton 25% .. Total she earned = \$9090 . 0.16x+0.25(30,000-x)=6060 0.16x+7500-0.25x=6060 -0.09x=-1440 x= -1440 / -0.09 x= \$ 16,000 with Dreyfus New leaders \$14,000 with Templeton
 Geometry_Word_Problems/323551: if a olympic swimming pool is twice as long as it is wide and ther perimeter is 150 meters then what are the lenght and width?1 solutions Answer 231575 by mananth(12270)   on 2010-07-19 09:18:42 (Show Source): You can put this solution on YOUR website!Let width be x Length = 2x .. Perimeter = 2*(L+B) 150= 2(x+2x) 150=6x x=150/6 x=25 meters width Length = 2x = 50 meters
 Average/323608: The average of 6 numbers is 10. If the average of 4 numbers is 12, then what is the average of the remaining 2 numbers? 1 solutions Answer 231571 by mananth(12270)   on 2010-07-19 08:58:54 (Show Source): You can put this solution on YOUR website!average of 6 numbers = 10 total of thses 6 numbers = 60. .. Average of 4 numbers is 12 total of 4 numbers = 40 .. difference of these totals is the total of balance 2 numbers 60-48 = 12 12 is the total of 2 numbers so the average = 12/2 = 6 .. Average of 2 numbers is 6
 Quadratic_Equations/323614: 40w^3-30w^2+5w1 solutions Answer 231560 by mananth(12270)   on 2010-07-19 08:37:07 (Show Source): You can put this solution on YOUR website!40w^3-30w^2+5w .. 5w(8w^2-6w+1) 5w(8w^2-4w-2w+1) 5w{4w(2w-1)-1(2w-1)} 5w(4w-1)((2w-1)
 Average/323609: The average age of boys & girls in a class is 10.5 yrs. That of the boys is 10.6 & that of the girls is 10.1. If there are 60 boys in the class how many girls are there? 1 solutions Answer 231556 by mananth(12270)   on 2010-07-19 08:32:26 (Show Source): You can put this solution on YOUR website!let the number of girls be x Number of boys = 60 Total students = x+60 Average age of class = 10.5 The total age of the class = 10.5(x+60) .. Average age of girls = 10.1 total age of girls = 10.1x .. Average age of boys = 10.6 Number of boys = 60 Total age of boys = 10.6*60= 636 years .. Total age of girls + total age of boys = Total age of class 10.1x+636=10.5(x+60) 10.1x +636=10.5x + 630 10.5x-10.1x = 636-630 0.4x= 6 x= 6/0.4 Multiply by 10 and divide by 10 x=60/4 x=15 girls
 Travel_Word_Problems/323611: find the distance traveled if you are going 38 miles per hour for 2 hours. (the answer will be in miles) 1 solutions Answer 231551 by mananth(12270)   on 2010-07-19 08:21:48 (Show Source): You can put this solution on YOUR website!Distance traveled = Rate * time rate = 38 mph time = 2hours Distance traveled in 2 hours = 38*2= 76 miles