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# Recent problems solved by 'mananth'

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 Percentage-and-ratio-word-problems/321527: Mr.Batti invested twice as much money in an account that pays 9% interest as he did in an account that pays 7% in interest. His total investment pays him 1,250 a year in interest. How much did he invest at each rate? THANKS.1 solutions Answer 230287 by mananth(12270)   on 2010-07-11 23:47:19 (Show Source): You can put this solution on YOUR website!let him invest x at 7% hw will invest 2x at 9% .. Interest equation 0.07x+0.09x=1250 multiply by 100 7x+9x=125000 16x=125000 x=125000/16 =7812.50 at 7% .. 2x= 2*7812.50 =15625.00 at 9%
 Mixture_Word_Problems/321528: A mixture of 14% disinfectant solution is to be made from 10% and 20% disinfected solutions. How much of each solution should be used if 20 gallons of 14% solutions are needed?1 solutions Answer 230286 by mananth(12270)   on 2010-07-11 23:38:23 (Show Source): You can put this solution on YOUR website!A mixture of 14% disinfectant solution is to be made from 10% and 20% disinfected solutions. How much of each solution should be used if 20 gallons of 14% solutions are needed? 10% solution be x gallons 20% solution will be 20-x gallons .. Total 14% solution 20 gallons .. Concentration eauation 0.1x+0.2(20-x)=20*0.14 0.1x+4-0.2x=2.8 -0.1x= -1.2 x= -1.2/ -0.1 x= 12 gallons of 10% solution Balance 8 gallons will be 20% solution
 Miscellaneous_Word_Problems/321557: Thank you Jim for your last answer. I really appreciate it!! Please help me solve this. Suppose it takes 3 days for a space vehicle to travel from earth to the moon. About how long would it take the same vehicle traveling at the same speed to reach Mercury? Moon--240,000 Mercury--57,000,000 Round to nearest whole number. Use scientific notation. 1 solutions Answer 230285 by mananth(12270)   on 2010-07-11 23:32:27 (Show Source): You can put this solution on YOUR website!Suppose it takes 3 days for a space vehicle to travel from earth to the moon. About how long would it take the same vehicle traveling at the same speed to reach Mercury? Moon--240,000 it takes 3 days so in 1 day it travels 240000/3 =80,000 8*10^4 /day Mercury--57,000,000 .. 5.7*10^7 is the distance of mercury. it will take 5.7*10^7 / 8*10^4 =712.5 days
 Number-Line/321567: -81+(-13)1 solutions Answer 230284 by mananth(12270)   on 2010-07-11 23:19:46 (Show Source): You can put this solution on YOUR website!-81+(-13) -81-13 = -94
 Rate-of-work-word-problems/321571: if one outlet pipe can drain a tank in 24 hours while a second outlet pipe can drain the same tank in 36 hours, how long will it take to drain the tank if both pipes are open?1 solutions Answer 230283 by mananth(12270)   on 2010-07-11 23:18:44 (Show Source): You can put this solution on YOUR website!if one outlet pipe can drain a tank in 24 hours while a second outlet pipe can drain the same tank in 36 hours, how long will it take to drain the tank if both pipes are open? draining the tank is 1 job. .. 1 drain does the job in 24 hours so it does 1/24 of the job in 1 hour. .. second does the job in 36 hours so it does 1/36 of the job in 1 hour .. together they do 1/24+1/36 of the job in 1 hour LCD = 72 = 3+2/72 =5/72 5/72 0f the job they do together in 1 hour 1 job they do in 72/5 hours =14.4 hours
 Evaluation_Word_Problems/321547: length of a rectangle is 3 m more than 5 times the width. the perimeter is 126 m. find the length and width?1 solutions Answer 230282 by mananth(12270)   on 2010-07-11 23:13:10 (Show Source): You can put this solution on YOUR website!let width be x length will be 5x+3 .. Perimeter = 2*L+2*W 2*x+2*(5x+3)=126 2x+10x+6=126 12x=120 x=10 the width length = 5x+3 =5*10+3 =50+3 =53
 Numeric_Fractions/321568: I cant get this for nothing 1/r = 1/R1 + 1/R2 :solve for R1 the R1 and R2 are subscripts 1 solutions Answer 230279 by mananth(12270)   on 2010-07-11 23:06:24 (Show Source): You can put this solution on YOUR website!1/r = 1/R1 + 1/R2 : .. 1/r-1/R2= 1/R1 .. R2-r/rR2 =1/R1 .. R1= rR2 /R2-r
 Equations/321570: I am having difficulty with solving and checking the following equation. Can you please help me? 7x-8(x+1) = 4(x+3)-3x1 solutions Answer 230277 by mananth(12270)   on 2010-07-11 23:02:30 (Show Source): You can put this solution on YOUR website!7x-8(x+1) = 4(x+3)-3x 7x-8x-8=4x+12-3x 7x-8x-4x+3x=8+12 -2x=20 x=20/-2 x=-10
 Percentage-and-ratio-word-problems/321569: Please help me solve this: Kayla paid 137.80, including 6% tax, for her calculator. How much did the calculator itself cost?1 solutions Answer 230275 by mananth(12270)   on 2010-07-11 22:58:58 (Show Source): You can put this solution on YOUR website!if 106 is the amount to be paid 100 will the price if 137.80 is paid then the price will be 137.80*100 / 106 =130 The price of calculator was 130
 Rectangles/321560: the primeter of a court is 114 the length is 6 more than two times the width what is the length and widty1 solutions Answer 230274 by mananth(12270)   on 2010-07-11 22:54:14 (Show Source): You can put this solution on YOUR website!let the width be x length = 2x+6 .. Perimeter = 2*L+2*w 2x+2(2x+6)=114 2x+4x+12=114 6x+12=114 6x=102 x=17 the width length = 2x+6 =2*17+6 =40 the length
 Problems-with-consecutive-odd-even-integers/321550: THE PRODUCT OF TWO CONSECUTIVE INTERGERS IS 71 MORE THAN THE SUM. FIND THE INTERGERS1 solutions Answer 230270 by mananth(12270)   on 2010-07-11 21:27:13 (Show Source): You can put this solution on YOUR website!let the integers be x & x+1 x(x+1)= x+x+1+71 x^2+x=2x+72 x^2-x-72=0 x^2-9x+8x-72=0 x(x-9)+8(x-9)=0 (x-9)(x+8)=0 x= 9 OR -8 the integers are 9,10 OR -9,-10
 Problems-with-consecutive-odd-even-integers/321357: The number 2002 is equal to the sum of 7 consecutive natural numbers. What is the smallest of these 7 numbers? A) 189 B) 186 C) 283 D) 289 E) 3061 solutions Answer 230159 by mananth(12270)   on 2010-07-11 07:29:32 (Show Source): You can put this solution on YOUR website!let the numbers be x,x+1,x+2,x+3,X=4,x+5,x+6 .. x+x+1+x+2+x+3+X=4+x+5+x+6 =2002 7x+21=2002 7x=2002-21 x=1981/7 x=283 .. The smallest number
 Numbers_Word_Problems/321332: I need help with the following word problem: The sum of a positive number and its square is 210. find the number. thank you!1 solutions Answer 230147 by mananth(12270)   on 2010-07-11 00:50:40 (Show Source): You can put this solution on YOUR website!let the number be x square of the number will be x^2 .. x^2+x=210 x^2+x-210=0 x^2+16x-15x-210=0 x(x+16)-15(x+16)=0 (x+16)(x-15)=0 x= -16 OR 15 x=15
 Expressions-with-variables/321331: can you show me step by step how to solve the following equation, I'm looking for the solution for x and y. 6x + 4y = 60 8x + 9y = -4 1 solutions Answer 230146 by mananth(12270)   on 2010-07-11 00:45:16 (Show Source): You can put this solution on YOUR website!6x + 4y = 60..............1 8x + 9y = -4..............2 Let us eliminate x by subtracting one equation from the other. before that you have to make the co-efficinets of x equal. multiply equation 1 by 8 and equation 2 by 6 . we get 48x +32y=480 48x+54y=-24 .. (48x+32y)-(48x+54y)=480-(-24) 48x+32y-48x-54y=504 -22y= 504 y=-22.91 plug the value of y in eq 1 x=((4*-22.91) -60)/-6 x=25.27
 Miscellaneous_Word_Problems/321330: Company A rents copiers for a monthly charge of \$200 plus 10 cents per copy. Company B rents copiers for a monthly charge of \$400 plus 5 cents per copy. What is the number of copies above which Company A's charges are the higher of the two? 1 solutions Answer 230144 by mananth(12270)   on 2010-07-11 00:25:09 (Show Source): You can put this solution on YOUR website!Company A rents copiers for a monthly charge of \$200 plus 10 cents per copy. Company B rents copiers for a monthly charge of \$400 plus 5 cents per copy. let thenumber of copies be x company A 200+0.1x Company B 400+0.05x .. 200+0.1x= 400+0.05x 0.05x = 200 x=200/0.05 x= 20000 After 20,000 copies company A becomes costly What is the number of copies above which Company A's charges are the higher of the two?
 Expressions-with-variables/321263: 1/a-b - 3ab/a^3-b^31 solutions Answer 230143 by mananth(12270)   on 2010-07-10 23:51:04 (Show Source): You can put this solution on YOUR website!1/a-b - 3ab/a^3-b^3 LCM = a^3-b^3 .. a^2+ab+b^2-3ab / a^3-b^3 a^2-2ab+b^2 / a^3-b^3 (a-b)^2 / (a-b)(a^2+ab+b^2) (a-b) / (a^2+ab+b^2)
 Numeric_Fractions/321285: I am having problems with my algebra homework! can you help me?1 solutions Answer 230141 by mananth(12270)   on 2010-07-10 23:35:29 (Show Source): You can put this solution on YOUR website!Try me
 Rate-of-work-word-problems/321294: Dixie can paint a room in 3 hours working alone. Trixie can paint the same room in 6 hours working alone. How long after Dixie starts to paint the room will it be finished if Trixie joins her 1 hour later?1 solutions Answer 230140 by mananth(12270)   on 2010-07-10 23:34:10 (Show Source): You can put this solution on YOUR website!Dixie can paint a room in 3 hours working alone. So she can do 1/3 of the job in 1 hour. Trixie can paint the same room in 6 hours So she can do 1/6 of the job in 1 hour. .. Trixie joins 1 hour late .. Dixie has done 1/3 of the job When Trixie joins only 1-1/3 of the job is remaining = 2/3 of the job. .. Together they do 1/3 +1/6 of the job in 1 hour. =2+1/ 6 =1/2 the job in 1 hour. .. 1/2 job they together do in 1 hour 2/3 of job they will do in 2/3 / 1/2 =2/3 * 2 1 1/3 hours They will finish the job in 1 1/3 hours.
 Expressions-with-variables/321311: the volume of a cube is given by V=s^3. where s is length of a side. find the length of a side of a cube if the volume is 500 cm^3. round to the answer to three decimal places. 7.937*7.937*7937=499.6............the answer is 7.937 1 solutions Answer 230137 by mananth(12270)   on 2010-07-10 23:10:21 (Show Source): You can put this solution on YOUR website!V=s^3 so s= sube root 500 s=7.937 cm
 Miscellaneous_Word_Problems/321327: The product of the page numbers on two facing pages of a book is 240. Find the page numbers. 1 solutions Answer 230136 by mananth(12270)   on 2010-07-10 23:07:52 (Show Source): You can put this solution on YOUR website!let the page number on the left side be x then page number on the right side will be x+1 The product = 240 x(x+1)=240 x^2+x=240 x^2+x-240=0 x^2+16x-15x-240=0 x(x+16)-15(x+16)=0 (x+16)(x-15)=0 x= -16 OR 15 Ignore the negative value. So the page numbers are 15 and 16
 Linear-equations/321317: Your friend is taking an algebra class that began one week after ours. Explain to your friend how by looking at two linear equations you can tell that corresponding lines are parallel and how you can tell that corresponding lines are perpendicular from the equations alone. 1 solutions Answer 230134 by mananth(12270)   on 2010-07-10 23:02:29 (Show Source): You can put this solution on YOUR website!write the equations in the form y=mx +c m is the slope of the line. Let the slope of one line be m1 Then the equation will be y=m1x+c .. Let the slope of the second line be m2 Write the equation of the second line in the same form y=m2x+c .. If m1 * m2 = -1 then the lines are perpendicular OR m1 = -1/m2
 Rectangles/321321: 37. A rectangular table is five times as long as it is wide. If the area is 180 ft^2, find the length and width of the table. 1 solutions Answer 230133 by mananth(12270)   on 2010-07-10 22:54:52 (Show Source): You can put this solution on YOUR website!let width be x feet length = 5x Area = 180 ft^2 .. Area of rectangle = L * W x^5x=180 5x^2=180 x^2=180/5 x^2=36 x=+ / - 6 Ignore the negative value. x=6 feet the width length = 5x = 5*6=30 feet
 Travel_Word_Problems/321168: Elena bicycles 6km/h faster than Carlos. In the same time it takes Carlos to bicycle 27km, Elena can bicycle 45km. How fast does each bicyclist travel?1 solutions Answer 230007 by mananth(12270)   on 2010-07-10 10:47:48 (Show Source): You can put this solution on YOUR website!Let Carlos's speed be x mph Elena bicycles 6km/h faster . x+6 mph Carlos cycles 27km, Elena can bicycle 45km. in the same time. time taken by carlos = time taken by Elena 27/x = 45 / x+6 45x=27(x+6) 45x=27x+162 45x-27x=162 18x= 162 x= 162/18 x=9 mph - Carlos'speed. 15 mph will be Elena's speed.
 Polynomials-and-rational-expressions/321171: Solve the equation and check your answer. q+5/3+q-5/5=10/31 solutions Answer 230002 by mananth(12270)   on 2010-07-10 10:09:29 (Show Source): You can put this solution on YOUR website!q+5/3 + q-5/5=10/3 .. LCM =15 5(q+5)+3(q-5) /15= 10/3 5q+25+3q-15 / 15 = 10/3 8q+10 /15=10/3 3(8q+10)=15*10 6(4q+5)=150 4q+5= 150/6 4q+5=25 4q=20 q=5 .. 5+5 / 3 + 5-5/3 10/3 +0 = 10/3
 Polynomials-and-rational-expressions/321169: Subtract. simplify if possible b/z+b-b/z-b=1 solutions Answer 229998 by mananth(12270)   on 2010-07-10 09:59:36 (Show Source): You can put this solution on YOUR website!b/z+b - b/z-b LCM = (z+b)(z-b) b(z-b)-b(z+b) bz-b^2-bz-b^2 / (z+b)(z-b) -2b^2/ (z+b)(z-b)
 Travel_Word_Problems/321170: i many mile an hour i must travel to get from springfield ill to cincinnati oh in less then six hour. I need to know how to do this. no just answers. the miles between the cities is 320. thank you please help.1 solutions Answer 229996 by mananth(12270)   on 2010-07-10 09:53:42 (Show Source): You can put this solution on YOUR website!distance = 320 miles time to be traveled less than 6 hours speed = distance / time 320/6 = 40 mph. you have to travel greater than 40mph to reach in less than 6 hours
 Money_Word_Problems/321159: If Ben invests \$4000 at 4% interest per year, how much additional money must he invest at 5.5% annual interest to ensure that the interest he receives each year is 4.5% of the total amount invested? 1 solutions Answer 229994 by mananth(12270)   on 2010-07-10 09:49:42 (Show Source): You can put this solution on YOUR website!If Ben invests \$4000 at 4% interest per year, how much additional money must he invest at 5.5% annual interest to ensure that the interest he receives each year is 4.5% of the total amount invested? .. let the additional amount to be invested be \$x at 5.5% \$4000 at 4% Total invested will be 4000+x , interest 4.5% .. Interest at 4% +interest at5.5% = iinterest at4.5% 0.04*4000+0.055x=0.045(4000+x) 160+0.055x=180+0.045x 0.055x-0.045x=180-160 0.010x=20 x= 20/0.010 \$ 2000 must be invested at 5.5%
 Volume/321165: How do you find the volume of a sphere?1 solutions Answer 229993 by mananth(12270)   on 2010-07-10 09:39:25 (Show Source): You can put this solution on YOUR website!The volume of the sphere is given by the formula V= 4/3 * pi*r^3 where V = volume & r is the radius of the sphere
 Rate-of-work-word-problems/321164: Helen earns \$7.50 an hour at her job, but if she works more than 35 hours in a week she is paid 1.5 times her regular salary for the overtime hours worked. One week her gross pay was \$352.50. How many overtime hours did she work that week?1 solutions Answer 229992 by mananth(12270)   on 2010-07-10 09:37:13 (Show Source): You can put this solution on YOUR website!Helen earns \$7.50 an hour at her job, but if she works more than 35 hours in a week she is paid 1.5 times her regular salary for the overtime hours worked. One week her gross pay was \$352.50. How many overtime hours did she work that week? .. If she works 35 hours she gets 35*7.50 = \$ 262.50 She got \$ 352.50 that week. so she got 352.50-262.50 = \$ 90 extra for overtime She gets 1.5 times for every extra hour so she gets 7.50*1.50= \$11.25 per extra hour .. The extra amount she got was \$ 90 so she worked for 90/11.25 extra hours = 8 hours over time
 Equations/321163: I am very confused, I have absolutely no idea how to solve this word problem. Please help me solve the problem: If Sally can paint a house in four hours, John can paint the same house in six hours. How long will it take them to paint it together?1 solutions Answer 229989 by mananth(12270)   on 2010-07-10 09:25:24 (Show Source): You can put this solution on YOUR website!Painting the house is considered as 1 job Sally can paint a house in four hours, so sally can do 1/4 of the job in 1 hour John can paint the same house in six hours. John can do 1/6 job in 1 hour . They together can do 1/4 + 1/6 of the job in 1 hour. 1/4 + 1/6 = 3+2 / 12 = 5/12 of the job in 1 hour so to do 1 job they take 12/5 hours = 2.4 hours They together can paint the house in 2.4 hours
 Travel_Word_Problems/321162: Two cyclist, 90 mi apart, start riding toward each other at the same time. One cycles twice as fast as the other. If they meet 2 h later, at what average speed is each cyclist traveling?1 solutions Answer 229986 by mananth(12270)   on 2010-07-10 09:19:38 (Show Source): You can put this solution on YOUR website!Two cyclist, 90 mi apart, start riding toward each other at the same time. One cycles twice as fast as the other. If they meet 2 h later, at what average speed is each cyclist traveling? .. let the speed of one cyclist be x mph the other will be 2x mph .. They both travel for 2 hours before they meet. .. distance traveled by one + distance traveled by other = Total distance between them when starting. .. 2x+2*2x=90 2x+4x=90 6x=90 x=15 mph the speed of first cyclist. The speed of second cyclist will be 2x = 2*15=30 mph