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# Recent problems solved by 'mananth'

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 real-numbers/370610: Find a number that is 68 greater than three times its opposite1 solutions Answer 264193 by mananth(12270)   on 2010-11-14 00:42:52 (Show Source): You can put this solution on YOUR website!Find a number that is 68 greater than three times its opposite .. Let the number be x .. the opposite of this number will be (-x) .. 3 times the opposite of the number = 3*(-x)=-3x .. add 68 we get (-3x)+68 x = (-3x+68) add 3x to both sides 3x+x=68 4x=68 .. divide by 4 4x/4 = 68/4 x= 17 the required number ... m.ananth@hotmail.ca
 Quadratic_Equations/370623: A common student error when solving a quadratic equation is simplifying incorrectly. Consider the following INCORRECT solution: 2+/- the square root of 7 divided by 2 = 1+/- square root of 7 Explain why x= 1+-sqrt7 is the incorrect solution. Is this not able to be factored any further from 2+-sqrt7/2 because the whole numerator needs divided by 2? 1 solutions Answer 264191 by mananth(12270)   on 2010-11-14 00:32:43 (Show Source): You can put this solution on YOUR website! .. you have youself answered the question.As you see above is in the numerator when you simplify each term in the numerator has to be divided by 2 = if you need to simplify further you have to use a calculator to write the answer in decimals. x= 1+3.228 x= 4.228 .. the same applies for the other root. ... m.ananth@hotmail.ca
 Money_Word_Problems/370576: Simone went to an outlet mall. Sweaters were \$5 each, shirts \$3, pairs of socks \$1. She spent \$70 and bought 26 items. She bought 1 more shirt than she did sweaters. Ignoring tax, set up a system of equations and solve the system.1 solutions Answer 264168 by mananth(12270)   on 2010-11-13 22:29:54 (Show Source): You can put this solution on YOUR website!Sweaters were \$5 each, shirts \$3, pairs of socks \$1. She spent \$70 and bought 26 items. She bought 1 more shirt than she did sweaters. Ignoring tax, set up a system of equations and solve the system. ... Sweaters were \$5 each, Let this number be x She bought 1 more shirt than she did sweaters. shirts \$3, : this will be x+1 Balance pair of socks = 26 - ( sum of shirts & sweaters) pairs of socks \$1.: this will be 26-(x+x+1) =26-(2x+1) She spent \$70 ... Price equation .... 5x+3(x+1)+1(26-(2x+1)) = 70 5x+3x+3+25-2x=70 6x+28=70 -28 -28 6x=42 /6 x=7... sweaters Shirts = x+1 = 8 Pair of socks = 26-(2x+1)= 26-(2*7+1)=26-15=11 ... CHECK 11*1+8*3+7*5=11+24+35=70 ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/370597: A rectangular solid has a base with length 5 cm and width 2 cm. If the volume of the solid is 100 cm3, find the height of the solid. [Hint: The volume of a rectangular solid is given by V = LWH.] Need help trying to figure this out Thank you1 solutions Answer 264159 by mananth(12270)   on 2010-11-13 21:54:14 (Show Source): You can put this solution on YOUR website!Vlome of the solid = 100 cm^3 .. Length = 5 cm Width = 2cm height = x .. Volume V = L*W*H V=5*2*x 5*2*x=100 10*x=100 /10 x= 10 cm the height ... m.ananth@hotmail.ca
 Volume/370595: i need to build a box to hold 300 cubic inches of ash, can you give me some inside deminsions for a rectangular box?1 solutions Answer 264156 by mananth(12270)   on 2010-11-13 21:45:07 (Show Source): You can put this solution on YOUR website!Volume of the box = 300 cu.in .. find the factors of 300 split the factors into suitable 3 parts to suit the requirement. .. 300 = 2*2*3*5*5 ... Since Volume V = L*W*H split the factors into 3 parts for the box to look practical. .. 2*5 by 2*3 by 5 height inches 10 by 6 by 5 in .. m.ananth@hotmail.ca
 Word_Problems_With_Coins/370599: May has 3 times as many dimes as nickels. In all she has \$1.40. How many coins of each type does she have? 1 solutions Answer 264154 by mananth(12270)   on 2010-11-13 21:37:28 (Show Source): You can put this solution on YOUR website!let her have x nickels dimes = 3x .. total money =\$ 1.40 = 140 cents ... 5x+10*3x=140 35x=140 /35 x=140/35 x = 4 the number of nickels .. dimes = 3x = 3*4 =12 .. CHECK 12*10+4*5 = 140 cents ... m.ananth@hotmail.ca
 Travel_Word_Problems/370512: Liz commutes 30 mi. to her job each day. She finds that if she drives 10 mi/h faster it takes her 6 minutes less to get to work. Find her new speed.1 solutions Answer 264146 by mananth(12270)   on 2010-11-13 21:08:44 (Show Source): You can put this solution on YOUR website!1/2 hour to work place every day speed = 30 mph ... if she increases her speed by 10 mph her speed will be 30+10 = 40 mph. ... let distance to work place be x .. time taken with present speed - time taken with increased speed = 1/10 hours .. t= d/r .. x/30 - x/(40)= 1/6 LCD = 120 (4x-3x)/120 = 1/6 x/120 =1/6 6x=120 /6 x= 20 miles distance to work .. m.ananth@hotmail.ca
 Money_Word_Problems/370578: total of 698 tickets were sold for an event. Three times as many gold (g) tickets were sold as silver (s) tickets. The total number of gold and silver tickets sold was twice the number of bronze (b) tickets sold. Set up equations, don't actually solve.1 solutions Answer 264142 by mananth(12270)   on 2010-11-13 21:00:37 (Show Source): You can put this solution on YOUR website!let number of silver tickets be s gold = g = 3s .. bronze = (3s+s)= 2b /2 b=4s/2 = 2s ... Total number of tickets = 698 ... s+g+b = s+3s+2s =698 =6s=698 ... m.ananth@hotmail.ca
 Travel_Word_Problems/370581: The riverboat Hiawatha goes 30 km upstream and back in 4 hours. If the Hiawatha's speed in still water is 16 km/h, what is the speed of the current? I set this problem up on a chart and had 30/16-r + 30/16+r = 4 and ended up getting r=16km/h. I am not quite sure if I set this problem up right. 1 solutions Answer 264134 by mananth(12270)   on 2010-11-13 20:51:48 (Show Source): You can put this solution on YOUR website!30/(16-r)+30/(16+r)=4 30(16+r)+30(16-r)/(256-r^2)=4 480+30r+480-30r/(256-r^2)=4 960=4(256-r^2) /4 240=256-r^2 r^2=256-240 r^2=16 Take the square root r = 4 mph. I think you forgot to take the square root since r^2=16 ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/370569: One pipe can fill a storage tank in five hours less time than a smaller second pipe can, and together they can fill it in six hours. How long would it take the larger pipe to fill it?1 solutions Answer 264122 by mananth(12270)   on 2010-11-13 20:20:20 (Show Source): You can put this solution on YOUR website!let second pipe take x hours to fill it will do 1/x of the job in 1 hour. .. First pipe takes 5 hour less than second pipe. x-5 hours .. it can do 1/(x-5) of the job in 1hour. ... Together they do the job in 6 hours.. together they do 1/6 of the job in hour. ... 1/x + 1/(x-5 ) = 1/6 .. LCD = x(x-5) (x-5+x)/(x(x-5))=1/6 (2x-5)/x(x-5) = 1/6 6(2x-5)=x(x-5) 12x-30=x^2-5x x^2-5x-12x+30=0 x^2-17x+30=0 x^2-15x-2x+30=0 x(x-15)-2(x-15)=0 (x-15)(x-2)=0 x= 2 OR 15 hours ... m.ananth@hotmail.ca
 Inverses/370540: The sum of a number and twice its multiplicative inverse (reciprocal) is 3. Find the number. 1 solutions Answer 264120 by mananth(12270)   on 2010-11-13 20:09:22 (Show Source): You can put this solution on YOUR website!x be the number reciprocal = 1/x 2 times reciprocal = 2/x ... x+2/x = 3 ... (x^2+2)/x=3 (x^2+2)=3x x^2-3x+2=0 x^2-2x-x+2=0 x(x-2)-1(x-2)=0 (x-2)(x-1)=0 x = 1 OR 2 ... m.ananth@hotmail.ca
 Age_Word_Problems/370552: May is M years old now. Six years ago, April was four less than thrice May's age then. Find April's present age. (Translating Word Phrases into Mathematical Expression)1 solutions Answer 264117 by mananth(12270)   on 2010-11-13 19:47:35 (Show Source): You can put this solution on YOUR website!May = m years .. 6 years ago May = m-6 years 3 times m-6 = 3(m-6) 4 less 3(m-6)-4 ... .. April =3(m-6)-4 ... m.ananth@hotmail.ca
 Circles/370545: Hi, I'm having trouble graphing the following parabola: It seems so simple. I have the vertex (0, 0) and I'm trying to find points and I'm getting the answer wrong. I found (32, 4) and (18, 3)...but these are apparently wrong. Please help! Thanks for your time :)1 solutions Answer 264116 by mananth(12270)   on 2010-11-13 19:44:07 (Show Source): You can put this solution on YOUR website! ... (0,0) (2,1) (2,-1) (8,-2) (8,+2) .. Plot the points and draw the curve. .. It ia a parabola opening to the right ... m.ananth@hotmail.ca
 Graphs/370541: can you help me graph the equation y=2over5x+2 on a graph please1 solutions Answer 264113 by mananth(12270)   on 2010-11-13 19:27:35 (Show Source): You can put this solution on YOUR website!y=2over5x+2 y= (2/5)x+2 generate values of y for different values of x and plot the points. ... (0,2) (5,4) (-5,0) .. ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/370543: 3x^3+2x^2+3x+21 solutions Answer 264111 by mananth(12270)   on 2010-11-13 19:21:02 (Show Source): You can put this solution on YOUR website!3x^3+2x^2+3x+2 .. x^2(3x+2)+1(3x+2) (x+1)(3x+2) ... m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/370343: Dipa has 7 more Rs.2 coins than 50 paisa coins. If the value of all the coins is Rs 76.50, find the number of each type of coins.1 solutions Answer 263971 by mananth(12270)   on 2010-11-13 06:48:29 (Show Source): You can put this solution on YOUR website!Dipa has 7 more Rs.2 coins than 50 paisa coins. If the value of all the coins is Rs 76.50, find the number of each type of coins. .. let 50 paise coins she has be x Rs.2 coins will be x+7 .. 50 paise = Rs. 0.5 .. Value Equation 0.5x+2(x+7)=76.50 0.5x+2x+14 = 76.50 2.50x=76.50-14 2.50x=62.50 divide by 2.50 x=62.50/2.50 x= 25 coins of 50 paise 25+7 = 32 coins of Rs.2 .. CHECK 32*2+25*0.5=76.5 ... m.ananth@hotmail.ca
 Average/370356: a canal boat travels 6 miles in 1 hr 30 mins. what is the average speed of the boat? give your answer in miles per hour.1 solutions Answer 263967 by mananth(12270)   on 2010-11-13 06:02:40 (Show Source): You can put this solution on YOUR website!1 hour 30 minutes = 6 miles =1 1/2 hour = 3/2 hours .. r=d/t r= (6 )/(3/2) r= 6*2/3 r=4 mph ... m.ananth@hotmail.ca
 Percentage-and-ratio-word-problems/370344: On a map, two cities are 3 ¾ inches apart. If 3/8 inches on the map represents 50 miles, find the number of miles between the cities. 1 solutions Answer 263966 by mananth(12270)   on 2010-11-13 06:00:08 (Show Source): You can put this solution on YOUR website!3/8 in = 50 miles ... 3 3/4 = 15/4 ... 15/4 will represent ? .. direct proportion ((15/4) *50)/(3/8) (325/2)/(3/8) (325/2)*(8/3) =433.33 miles ... m.ananth@hotmail.ca
 Numbers_Word_Problems/370350: seventeen greater than a number is 199. find the number 1 solutions Answer 263965 by mananth(12270)   on 2010-11-13 05:54:39 (Show Source): You can put this solution on YOUR website!let number be x 17 greater = x+17 .. x+17 = 199 -17 -17 x=199-17 x=182 ... m.ananth@hotmail.ca
 Travel_Word_Problems/370351: A train is going to a place B and the velocity is 80 km/h. After half an hour another train leaves for B and its velocity is 100 km/h. the trains arrive in B at the same time. what is the lengh of the route ? plz help1 solutions Answer 263964 by mananth(12270)   on 2010-11-13 05:53:11 (Show Source): You can put this solution on YOUR website!A train is going to a place B and the velocity is 80 km/h. After half an hour another train leaves for B and its velocity is 100 km/h. the trains arrive in B at the same time. what is the lengh of the route ? plz help ... Let the distance be x km .. Train 1 speed = 80 km/h in 1/2 hour it would have traveled 40 km. ... This is when train 2 leaves A .. the time taken by train1 to travel x-40 km= time taken by train B to travel x km. .. speed of train 1 =80km/h time train 1 = (x-40)/80 ... speed of train2 = 100 km/h distance = x .. time train2 = x/100 ... x/100 = (x-40)/80 80x=100(x-40) 80x=100x-4000 100x-80x= 4000 20x=4000 /20 x= 200 km the length of the route. ... m.ananth@hotmail.ca
 Circles/370352: find the area of the largest circle which can be cut from a square of 4edge 4 in. what is the area of the material wasted?1 solutions Answer 263963 by mananth(12270)   on 2010-11-13 05:46:32 (Show Source): You can put this solution on YOUR website!square edge = 4 in. Area of square = L^2 = 4*4 = 16 sq.in ... the center of the square will be the center of the circle. so radius = 2 .. area of circle = pi*r^2 A= pi*2^2 A=4pi A= 12.56 sq.in .. The wasted area = area of square - area of circle =16-12.56 =3.44 sq.in ... m.ananth@hotmail.ca
 Linear-equations/370355: find the equation of a line perpendicular to the line x=4 and passes thrugh the point ( 4, 2 )1 solutions Answer 263962 by mananth(12270)   on 2010-11-13 05:41:41 (Show Source): You can put this solution on YOUR website!x=4 is a line parallel to y axis ... the required equation will be y =2 .. this will be parallel to the x axis and will intersect at (4,2) .. m.ananth@hotmail.ca
 Percentage-and-ratio-word-problems/370353: 1) A fish can swim at 14m/s with the current and at 6m/s against it. Find the speed of the current and the speed of the fish in still water. 2) If the numerator and denominator of a fraction are both decreased by one the fraction becomes 2/3. If the numerator and denominator are both increased by one the fraction becomes 3/4. Find the original fraction. 1 solutions Answer 263961 by mananth(12270)   on 2010-11-13 05:32:11 (Show Source): You can put this solution on YOUR website!let speed of fish in still water be x let speed of current be y m/s .. x+y =14 x-y =6 add the equations 2x=20 /2 x= 10 m/s y = 4m/s ... m.ananth@hotmail.ca ... let the numerator be x denominator be y ... (x-1)/(y-1) =2/3 3(x-1)=2(y-1) 3x-3=2y-2 3x-2y =1.................1 ... (x+1)/(y+1)=3/4 4(x+1)=3(y+1) 4x+4 = 3y+3 4x-3y=-1................2 multiply equation 1 by -3 & equation (2) by 2 -9x+6y=-3 8x-6y=-2 add i -x=-5 x=5 .. plug value of x in (1) 3*(5)-2y = 1 -2y= -14 /-2 y=7 .. Fraction = 5/7 ... m.ananth@hotmail.ca
 Numeric_Fractions/370354: what is 4a-20 over a2(squared) - 25 simplified fully ?1 solutions Answer 263960 by mananth(12270)   on 2010-11-13 05:06:49 (Show Source): You can put this solution on YOUR website! .... (a-5) cancel off ... m.ananth@hotmail.ca
 Rate-of-work-word-problems/370254: Caleb is having a very hard time coming up with ideas for math problems. He normally comes up with them at a rate of three per hour, but when he starts listening to music he slows down to a rate he cannot determine. today he has to make up twelve problems. He alterates between one hour with the music and one hour without, starting with it on. If it takes him 5 hours to complete the problems, how many problems can he make up in an hour while listening to music?1 solutions Answer 263929 by mananth(12270)   on 2010-11-12 22:36:18 (Show Source): You can put this solution on YOUR website!without music = 3 per hour total 12 problems completion time = 5 hours .. Starts with music on 3 hours music on and 2 hours without music. In 2 hours he will do 2*3 = 6 problems. Balnce 6 problems in 3 hours so with music he does 2 problems per hour. ... m.ananth@hotmail.ca
 Geometry_Word_Problems/370283: the perimeter of a rectangle is 116m. the length is 7 m more than twice the width. find the dimensions1 solutions Answer 263924 by mananth(12270)   on 2010-11-12 22:30:23 (Show Source): You can put this solution on YOUR website!let width be x length = 2x+7 ... Perimeter = 2L+2W 2x+2(2x+7)=116 .. 2x+4x+14=116 6x+14=116 -14 -14 6x=116-14 6x=102 /6 x= 102/6 x= 17 m the width. Length = 2*17+7 = 41 m ... m.ananth@hotmail.ca
 Rate-of-work-word-problems/370282: an experienced painter can paint a picket fence in 20 hours. An apprentice painter can do the same job in 45 hours. How long would it take to paint the fence of both painters worked together?1 solutions Answer 263919 by mananth(12270)   on 2010-11-12 22:26:30 (Show Source): You can put this solution on YOUR website!Painter takes 20 hours so he will do 1/20 of the job in 1 hour .. Apprentice takes 45 hours so he does 1/45 of the job in 1 hour. .. together they do 1/20 + 1/45 of the job in 1 hour =(9+4)/180 =13/180 of the job in 1 hour so they will together take 180/13 hours to do the job .. 13.8 hours ... m.ananth@hotmail.ca
 Problems-with-consecutive-odd-even-integers/370249: Grant is thinking of two numbers. He says that one of the numbers is six times the other number decreased by 2 and the sum of the numbers is 25. What are the numbers?1 solutions Answer 263897 by mananth(12270)   on 2010-11-12 20:29:42 (Show Source): You can put this solution on YOUR website!Grant is thinking of two numbers. He says that one of the numbers is six times the other number decreased by 2 and the sum of the numbers is 25. What are the numbers? .. let thenumbers be x & y x+y =25......................1 .. x=6y-2 x-6y=-2......................2 .. multiply equation1 by -1 we get -x-y=-25 add it to (2) -6y-y=-25-2 -7y=-27 y=3.85 plug value of y in (1) x+3.85=25 x=25-3.85 we get x= 21.15 .. m.ananth@hotmail.ca
 Money_Word_Problems/370252: black pencils sell at two for 15 cents, and red pencils sell at 10 cents each. How many of each kind were sold if a total of 25 were sold for \$2.00?1 solutions Answer 263895 by mananth(12270)   on 2010-11-12 20:17:27 (Show Source): You can put this solution on YOUR website!black pencils sell at two for 15 cents, and red pencils sell at 10 cents each. How many of each kind were sold if a total of 25 were sold for \$2.00? .. black pencils two for 15 cents, so 1 for 7.5 cents red pencils 10 cents each. total of 25 were sold for \$2.00 = 200 cents ... let black pencils be x numbers red pencils will be 25-x .. cost of black pencils = 7.5x cost of red penci;s = 10(25-x) .. 7.5x+10(25-x)=200 7.5x+250-10x= 200 -2.5x=-250+200 -2.5x=-50 /-2.5 x= -50/-2.5 x=20 pencils ---- black 5 will be red ... m.ananth@hotmail.ca ..
 Percentage-and-ratio-word-problems/370251: Coffee beans from 14 trees are required to produce the 17lbs of coffee that the average person in the U.S. drinks each year. How many trees are required to produce 375lbs of coffee?1 solutions Answer 263894 by mananth(12270)   on 2010-11-12 20:11:37 (Show Source): You can put this solution on YOUR website!17 pounds are produced from 14 trees 375 pounds will require ? this is direct proportion .. number of trees = 375* 14/17 = 308.8 =309 trees are required .. m.ananth@hotmail.ca
 Travel_Word_Problems/370236: The speed of the boat in still water is 28 mph. the boat traveled 70 miles per hour downstream in the same amount of time that it took to travel 42 miles upstream. What is the rate of current of the river?1 solutions Answer 263893 by mananth(12270)   on 2010-11-12 20:07:57 (Show Source): You can put this solution on YOUR website!The speed of the boat in still water is 28 mph. the boat traveled 70 miles per hour downstream in the same amount of time that it took to travel 42 miles upstream. What is the rate of current of the river? .. let rate of current be x mph rate of boat in still water = 28mph .. Upstream rate = 28-x mph downstream rate = 28+x .. upstream distance = 42 miles downstream distance = 70 miles ... t= d/r upstream time = downstream time ... 42/(28-x) = 70/x 42x=70(28-x) 42x=1960-70x 42x+70x=1960 112x=1960 /112 x= 1960/112 x= 17.5 mph. the rate of current ... m.ananth@hotmail.ca