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# Recent problems solved by 'mananth'

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 Word_Problems_With_Coins/514257: sumitra has Rs 34 in 50 paise and 25 paise coins. If the number of 25 paise coins is twice the number of 50 paise coins , how many coins of each kind does she have.1 solutions Answer 343381 by mananth(12270)   on 2011-10-13 08:48:02 (Show Source): You can put this solution on YOUR website!50 paise coins = x 25 paise coins = 2x She has Rs34 = 3400 paise 50*x+25(2x)=3400 50x+50x=3400 100x=3400 x=3400/100 x= 34 ---- 50 paise coins 25 paise coins ---- 34*2= 68 CHECK 68*25 + 34*50 = 3400 m.ananth@hotmail.ca
 Travel_Word_Problems/514306: karen left her house heading east and her sister left two hours later heading west at a rate of 5mph faster than Karen. Six hours after Karen left, she and her sister were 600 miles apart. How fast was Karen moving?1 solutions Answer 343380 by mananth(12270)   on 2011-10-13 08:42:18 (Show Source): You can put this solution on YOUR website!Karen speed = x time she traveled = 6 hours so she traveled 6x miles Sister speed = x+5 mph time she traveled = 4 hours so she traveled 4(x+5) miles 4(x+5)+6x=600 4x+20+6x=600 10x=580 x=580/10 x= 58 mph 58*6=348 63*4=252 Total = 600 m.ananth@hotmail.ca
 Travel_Word_Problems/514279: a river is flowing at a rate of 5kph a boat travels 12km upstream and 36 km downstream in a total of 9hrs.what is the speed of the boat in stilll water?1 solutions Answer 343379 by mananth(12270)   on 2011-10-13 08:34:14 (Show Source): You can put this solution on YOUR website!Boat speed x mph current speed 5 mph Distance with current 36 miles Distance against current 12 miles spee with current x + 5 mph spee against current= x -5 mph Total time = 9 hours Time with current= 36 /( x + 5 ) time against current 12 / ( x -5 ) Time with current + time against = 9 hours 36/(x + 5 ) + 12 /(x -5 ) = 9 LCD = ( x + 5 )* (x -5 ) multiply the equation by the LCD we get 3*(x -5)+ 12 (x +5)= 9 (x^2 -25 ) 36)x -180 + 12 x + 60 ) = 9 X^2 -225 48 x -120 = 9 X^2 -225 9 X^2 -48 x 120 + -225 = 0 9 X^2+ -48 x+ -105 = 0 / 9 1 X^2 -5.33 x -11.67 = 0 Find the roots of the equation by quadratic formula a= 1 ,b= -5.33 ,c= -11.67 b^2-4ac= 28.41 + 46.68 b^2-4ac= 75.09 49.98 x1=( 5.33 + 8.67 )/ 2 x1= 7 7 x2=( 5.33 -8.67 ) / 2 x2= -1.67 Ignore negative value Boat speed = 7 mph
 Money_Word_Problems/514239: Francisco R Designs makes T-shirts at \$4.25 a shirt but charges a set up fee of \$50.00. His competitor Gary Ray Signs charges \$6.70 a shirt but has a set up fee of \$20.00. If yuo are in charge of ordering shirts for your school club, when would it be beneficial to order shirts from Francisco R Designs? Construct two distinct equations: one for Francisco R Designs and one for Gary Ray Signs. 1 solutions Answer 343354 by mananth(12270)   on 2011-10-13 02:33:11 (Show Source): You can put this solution on YOUR website!Let x be the number of shirts Francisco R, C(f)= 50 + 4.25 x Gary Ray, C(g)= 20 + 6.70 x Francisco R < Gary Ray C(r) 20 + 6.70 x < 50 + 4.25 x 20 + 6.70 x < 50 + 4.25 x 20 - 50 < 4.25 x -6.7 x -30 < -2.45 x 12.24 < x The quantity should be greater than 13 shirts m.ananth@hotmail.ca
 Linear-systems/514248: Solve for x: 2x+1/x-3 = 4x+6/2x+3 Explain steps for me please? i like to see where ya get numbers from and/or what you did exactly. Thank you, in advance! :)1 solutions Answer 343353 by mananth(12270)   on 2011-10-13 02:22:21 (Show Source): You can put this solution on YOUR website! Cross multiply (2x+1)(2x+3)=(4x+6)(x-3) 2x(2x+3)+1(2x+3)=4x(x-3)+6(x-3) 4x^2+6x+2x+3=4x^2-12x+6x-18 14x=-21 x=-21/14 x=-3/2 m.ananth@hotmail.ca
 Rectangles/514085: the width of a rectangle is 12 ft less than the length. the area of the rectangle is 540 square ft. Find the dimensions of the rectangle1 solutions Answer 343282 by mananth(12270)   on 2011-10-12 21:00:30 (Show Source): You can put this solution on YOUR website!length = x width = (x-12) Area = L*W Area = x(x-12)=540 x^2-12x=540 x^2-12x-540=0 x^2-30x+18x-540=0 x(x-30)+18(x-30)=0 (x-30)(x+18)=0 x=30 which is positive length = 30 ft width = 18 feet m.ananth@hotmail.ca
 Linear-systems/514072: A thin 30cm candle takes 3h to burn from one end to the other. A thicker candle with the same length takes 5h to burn from one end to the other. If the thicker candle is lit at 7pm, and the thin candle is lit 30 min later, at what time will the candles be at the same height?1 solutions Answer 343280 by mananth(12270)   on 2011-10-12 20:56:02 (Show Source): You can put this solution on YOUR website!Thin candle burning rate is 30/3 = 10 cm/h Thick candle burning rate = 30/5 = 6 cm/h Thin candle burns 10-6 = 4 cm/h faster than thick candle Thicker candle is lit at 7 thinner candle is lit at 7.30 so difference = 1/2 hour. in 1/2 hour the thin candle would have burnt 10*1/2 = 5 cm time both will have same height = difference in length when second candle is lighted / difference between burning rates 5/4 = 1.25 hours m.ananth@hotmail.ca
 Circles/514052: Find an equation for the line that bisects the given quadrants. (Give your answer in slope intercept form.) II and IV 1 solutions Answer 343277 by mananth(12270)   on 2011-10-12 20:39:32 (Show Source): You can put this solution on YOUR website!Consider the equation y= mx+b Since the line bisects two Quadrants It passes through the origin. the y intercept is =0 so the equation will be y=x but the line will be from left to right sloping downwards passing the IV quadrant. so it will have negative slope The equation will be y=-x
 Linear-equations/513996: write an equation of the line that passes through (6,7) and has a slope (m) of 8?1 solutions Answer 343275 by mananth(12270)   on 2011-10-12 20:26:11 (Show Source): You can put this solution on YOUR website!m= 8 Plug value of the slope and point ( 6 , 7 ) in Y = m x + b 7.00 = 48 + b b= 7 - 48 b= -41 So the equation will be Y = 8 x -41 m.ananth@hotmail.ca
 Equations/514004: What is the answer of 5a-9a? Thanks!1 solutions Answer 343274 by mananth(12270)   on 2011-10-12 20:23:53 (Show Source): You can put this solution on YOUR website!5a-9a= -4a
 Travel_Word_Problems/514053: Kent drives his Mazda 150 miles in the same time that it takes Dave to drive his Nissan 135 miles. If Kent averages 5 miles per hour faster than Dave, find their rates. 1 solutions Answer 343273 by mananth(12270)   on 2011-10-12 20:19:50 (Show Source): You can put this solution on YOUR website!Dave x mph Kent 5 faster = x+ 5 Dave 135 miles Kent 150 miles Dave time = Kent time t=d/r 135 / x = 150 /( x + 5 ) cross multiply 135 ( x + 5 ) = 150 x 135 x + 675 = 150 x 150 x - 135 x = 675 15 x = 675 / 15 x = 45 mph Dave 50 mph Kent m.ananth@hotmail.ca
 Linear-equations/514049: equation for the line that passes through the points (-4,-8) and (8,4)1 solutions Answer 343270 by mananth(12270)   on 2011-10-12 20:15:02 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 -4 -8 8 4 slope m = (y2-y1)/(x2-x1) ( 4 - -8 )/( 8 - -4 ) ( 12 / 12 ) m= 1 Plug value of the slope and point ( -4 , -8 ) in Y = m x + b -8.00 = -4 + b b= -8 - -4 b= -4 So the equation will be Y = x -4
 Graphs/514048: Please help I am lost. write the equation in standard form using only integers and positive coefficient for x. y+1/6=1/3(x-4)1 solutions Answer 343268 by mananth(12270)   on 2011-10-12 20:11:49 (Show Source): You can put this solution on YOUR website! the LCD of the equation is 12 multiply each term by 12 12y+2=4(x-4) 12y+2=4x-16 -4x+12y=-18 4x-12y=18 m.ananth@hotmail.ca
 Mixture_Word_Problems/513657: a merchant has coffee worth \$60 a pound that she wishes to mix with 50 pounds of coffee worth \$90 a pound to get a mixture that can be sold for \$70 a pound. How many pounds of the \$60 coffee should be used?1 solutions Answer 343070 by mananth(12270)   on 2011-10-12 09:39:00 (Show Source): You can put this solution on YOUR website! --------price ---------------- quantity Coffee I 90 ---------------- 50 lbs coffee II 60 ---------------- x lbs Mixture 70 ---------------- 50 + x lbs 90*50+60 x=70(50 +x) 4500+60 x=3500 + 70 x 60 x + -70 x = 3500 - -4500 -10 x = -1000 / -10 x = 100 100 lbs of 60 % coffee II
 Percentage-and-ratio-word-problems/513644: a certain metal is 30% tin. how many kilograms of this metal must be mixed with 70 kg of a metal that is 70% tin to get a metal that is 50% tin?1 solutions Answer 343069 by mananth(12270)   on 2011-10-12 09:35:31 (Show Source): You can put this solution on YOUR website! --------percent ---------------- quantity Tin I 70 ---------------- 70 Kgs Tin II 30 ---------------- x Kgs Mixture 50 ---------------- 70 + x Kgs 70*70+30 x= 50 ( 70 + x ) 4900 + 30x = 3500 + 50 x 30 x + -50 x = 3500 - -4900 -20 x = -1400 / -20 x = 70 70 Kgs of 30 % Tin II
 Rational-functions/513537: 14x + 12y =562 x + y =421 solutions Answer 343046 by mananth(12270)   on 2011-10-12 04:12:50 (Show Source): You can put this solution on YOUR website!14 x + 12 y = 562 .............1 1 x + 1 y = 42 .............2 Eliminate y multiply (1)by 1 Multiply (2) by -12 14 x 12 y = 562 -12 x -12 y = -504 Add the two equations 2 x = 58 / 2 x = 29 plug value of x in (1) 14 x + 12 y = 562 406 + 12 y = 562 12 y = 562 -406 12 y = 156 y = 13
 Linear-systems/513553: Help! Please, Linear Combinations 0.5x + 2.2y = 9 6x + 0.4y = -221 solutions Answer 343045 by mananth(12270)   on 2011-10-12 04:09:06 (Show Source): You can put this solution on YOUR website!0.5x + 2.2y = 9 6x + 0.4y = -22 multiply both equations by 10 5x+22y=90 60x+4y=-220 5 x + 22 y = 90 .............1 60 x + 4 y = -220 .............2 Eliminate y multiply (1)by -4 Multiply (2) by 22 -20 x -88 y = -360 1320 x 88 y = -4840 Add the two equations 1300 x = -5200 / 1300 x = -4 plug value of x in (1) 5 x + 22 y = 90 -20 + 22 y = 90 22 y = 90 + 20 22 y = 110 y = 5
 Numbers_Word_Problems/513571: Please help me to answer this question 1/3 a number is smaller than twice the number by 30. what is the number ? 1 solutions Answer 343044 by mananth(12270)   on 2011-10-12 04:04:30 (Show Source): You can put this solution on YOUR website!let the number be x twice the number = 2x 2x- 1/3 x =30 multiply by 3 6x-x=90 5x=90 /5 x=18
 Polynomials-and-rational-expressions/513574: use factoring to solve the quadratic equation x(x-2)^3 - 35(x-2)^2 =01 solutions Answer 343043 by mananth(12270)   on 2011-10-12 04:01:57 (Show Source): You can put this solution on YOUR website!x(x-2)^3-35(x-2)^2=0 x(x-2)^3=35(x-2)^2 divide by (x-2)^2 x(x-2)=35 x^2-2x=35 x^2-2x-35=0 x^2-7x+5x-35=0 x(x-7)+5(x-7)=0 (x-7)(x+5)=0 x=7 OR -5
 Linear-equations/512925: find the equation of the line that goes through the given point and has the given slope (2,5), 4 1 solutions Answer 342824 by mananth(12270)   on 2011-10-11 10:44:29 (Show Source): You can put this solution on YOUR website!(2,5) slope =4 y=mx+b plug slope and point 5=8+b b=-3 so the equation will be y=4x-3
 Linear-equations/512899: I need help putting these in slope intercept form (-1,7) and (-2,-15)1 solutions Answer 342823 by mananth(12270)   on 2011-10-11 10:41:49 (Show Source): You can put this solution on YOUR website!x1 y1 x2 y2 -1 7 -2 -15 slope m = (y2-y1)/(x2-x1) ( -15 - 7 )/( -2 - -1 ) ( -22 / -1 ) m= 22 Plug value of the slope and point ( -1 , 7 ) in Y = m x + b 7.00 = -22 + b b= 7 - -22 b= 29 So the equation will be Y = 22 x + 29 m.ananth@hotmail.ca
 Average/512972: I need to simplify by removing factors of 1..... p^2-25/p^2-10p+251 solutions Answer 342820 by mananth(12270)   on 2011-10-11 10:36:07 (Show Source): You can put this solution on YOUR website!p^2-25/p^2-10p+25 m.ananth@hotmail.ca
 Travel_Word_Problems/512928: A tank contains 60 gallons of 50% solution of glycerin and water. What volume of water must be added to the solution to reduce glycerin concentration to 12%?1 solutions Answer 342800 by mananth(12270)   on 2011-10-11 09:41:02 (Show Source): You can put this solution on YOUR website! --------percent ---------------- quantity glycerin 50 ---------------- 60 gallons water 0 ---------------- x gallons Mixture 10 ---------------- 60 + x gallons 50 * 60 + 0 x = 10 ( 60 + x ) 3000 + 0 x = 600 + 10 x 0 x + -10 x = 600 - -3000 -10 x = -2400 / -10 x = 240 240 gallons of water
 Graphs/512929: Can you please help me graph this linear inequalities y<6x+21 solutions Answer 342798 by mananth(12270)   on 2011-10-11 09:36:45 (Show Source): You can put this solution on YOUR website!y>6x+2 First determine the boundary of the inequality The boundary y=6x+2 when x=0 y=2 (0,2) when y=0, x=-2/3 =-1/3 (-1/3,0) Since y > than something the upper side of the line will be shaded. The line will be dotted m.ananth@hotmail.ca
 Geometry_Word_Problems/512873: Three squares with areas of 150 cm2, 54 cm2, and 24 cm2 are displayed on a computer monitor. What is the sum (in radical form) of the perimeters of these squares1 solutions Answer 342781 by mananth(12270)   on 2011-10-11 04:42:32 (Show Source): You can put this solution on YOUR website!square I Area = 150 = perimeter = Perimeter = square II area =54 side = side = perimeter = Add them up Total perimeter = =cm m.ananth@hotmail.ca
 Trigonometry-basics/512876: Two buildings A and B adjacent to each other are separated by a narrow alley. Building A has a window at a heights of 12 meters and building B has a winder at a height of 8 meters, both windows facing the alley. A 13meter ladder placed in the alley leaning on the wall of building A reaches the winder at a height of 12meters from the ground. Without changing the position of the base of the ladder, the ladder is tilted towards building B and is able to just reach the winder at 8meters. What is the width of the alley?1 solutions Answer 342780 by mananth(12270)   on 2011-10-11 04:32:58 (Show Source): You can put this solution on YOUR website!let the foot of the ladder be located at M let the distance on ground from ladder foot to base of building A be MA let the distance on ground from ladder foot to base of building B be MB MA^2= 13^2-12^2 MA^2= 169-144=25 MA=5 m ... MB^2= 13^2-8^2 MB^2=169-64 MB^2= 105 MB= 10.25 m MA + MB = alley width 5+10.25= 15.25 m m.ananth@hotmail.ca
 Surface-area/512870: A rectangular block of land is 240m x 180m in size. A well of uniform diameter 14m and 20m depth is dug in the middle of the block and the soil dug out is evenly spread over the remaining area of the land. What will be the increase in the height of the block?1 solutions Answer 342763 by mananth(12270)   on 2011-10-11 02:33:27 (Show Source): You can put this solution on YOUR website!diameter of well = 14 m, radius = 7 depth = 20 m Volume of mud dug out = pi*r^2*h V= 3.14*7^2*20 V= 3077.2 m^3 Area of Land = 240* 180 = 43200 sq. m Volume of the land after filling = L*W*H dug out mud is the volume increase 3077.2 = 43200*H H=3077.2/43200 H= 0.0712 m 0.0712 *100 = 7.12 cm The height will increase by 7.12 cm m.ananth@hotmail.ca
 Age_Word_Problems/512871: At present a mother is 9 times as old as her daughter. 5 Years later, the daughter's age will be 1/5th of the age of the mother. Calculate their current ages. 1 solutions Answer 342762 by mananth(12270)   on 2011-10-11 02:24:24 (Show Source): You can put this solution on YOUR website!daughter = x years mom=9x after 5 years daughter = x+5 years Mom = 9x+5 years 1/5(9x+5)=x+5 9x+5= 5(x+5) 9x+5=4x+25 9x-4x=25-5 5x=20 /4 x=4 daughter's age mom's age = 9*4 = 36 years m.ananth@hotmail.ca
 Linear-systems/512802: solve the system of equations by graghing x+2y=2 2x+4y=361 solutions Answer 342761 by mananth(12270)   on 2011-10-11 02:09:36 (Show Source): You can put this solution on YOUR website!x+2y=2...........1 2x+4y=36...........2 equation1 when x= 0 y= 1 ( 0 , 1 ) when y = 0 x= 2 ( 2 , 0 ) Equation 2 when x= 0 y= 9 ( 0 , 9 ) when y = 0 x= 18 ( 18 , 0 ) You will observe that the graphs have same slope and different intercepts. So the lines are parallel to each other. m.ananth@hotmail.ca
 Distributive-associative-commutative-properties/512801: I need help with algebra for my 7th grade son:( example algebra properties 3(5+1) I have no idea what to do? THNX Marlen desperate mom!!1 solutions Answer 342758 by mananth(12270)   on 2011-10-11 01:47:38 (Show Source): You can put this solution on YOUR website!let me try 3(5+1) This means 3 x (5+1) 3 x 6 =18 m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/512803: Hello, I am in Algebra II. There are two positive numbers with the following properties. 1. The first number is 4 more than the second number. 2. The product of the two numbers is 4 more than their sum. What could these two numbers be?1 solutions Answer 342757 by mananth(12270)   on 2011-10-11 01:45:42 (Show Source): You can put this solution on YOUR website!one number be x Other number will be x+4 The product = x(x+4) x(x+4)=4+(x+x+4) x^2+4x=2x+8 x^2-2x+4x-8=0 x^2+2x-8=0 x^2+4x-2x-8=0 x(x+4)-2(x+4)=0 (x+4)(x-2)=0 x=-4 OR 2 The numbers are (-4,0) , (2,6) m.ananth@hotmail.ca