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# Recent problems solved by 'mananth'

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 Money_Word_Problems/683587: A person invested \$20,000, part at an interest rate of 6% annually and the remainder at 7% annually. The total interest at the end of 1 year was equivalent to an annual 6.75% rate on the entire \$20,000. How much was invested at each rate? 1 solutions Answer 423623 by mananth(12270)   on 2012-11-21 06:52:41 (Show Source): You can put this solution on YOUR website!6.75% on 20,000 = 1350 total interest earned. Part I 6.00% per annum ------------- Amount invested =x Part II 7.00% per annum ------------ Amount invested = y 20000 Interest----- 1350 Part I 6.00% per annum ---x Part II 7.00% per annum ---y Total investment x + 1 y= 20000 -------------1 Interest on both investments 6.00% x + 7.00% y= 1350 Multiply by 100 6 x + 7 y= 135000.00 --------2 Multiply (1) by -6 we get -6 x -6 y= -120000.00 Add this to (2) 0 x 1 y= 15000 divide by 1 y = 15000 Part I 6.00% \$ 5000 Part II 7.00% \$ 15000 CHECK 5000 --------- 6.00% ------- 300.00 15000 ------------- 7.00% ------- 1050.00 Total -------------------- 1350.00 m.ananth@hotmail.ca
 Age_Word_Problems/683583: Two years ago, the sum of the ages of a boy and his sister is 20 years. Three years from now, their ages will differ by 10 years. Form a pair of linear equations and find their present age.1 solutions Answer 423622 by mananth(12270)   on 2012-11-21 06:43:03 (Show Source): You can put this solution on YOUR website!Let the boy's age bex girls age be y 2 years ago their ages x-2 boy's age y-2 girls age (x-2)+(y-2)=20 x+y-4=20 x+y=16...................(1) 3 years hence their ages will be x+3 & y+3 (x+3)-(y+3)=10 x-y=10.................(2) Add (1) & (2) 2x= 26 x= 13 the boy's age Girls age = 20-13=7 Their ages could be 13 & 7
 Inequalities/683577: 1 solutions Answer 423621 by mananth(12270)   on 2012-11-21 06:33:32 (Show Source): You can put this solution on YOUR website! Multiply by 2 add -4
 �t�e�s�t/683560: Dear tutors, please help me answer: solve for a: a/x + b/y = a/y1 solutions Answer 423617 by mananth(12270)   on 2012-11-21 03:38:50 (Show Source): You can put this solution on YOUR website! LCD = xy (ay-ax)/xy = -b/y (ay-ax)= (xy)(-b/y) a(y-x) =(xy)(-b/y) a= (xy)(-b/y)/(y-x)
 Equations/683544: 2x+3y=200 5x+4y+2901 solutions Answer 423616 by mananth(12270)   on 2012-11-21 03:35:02 (Show Source): You can put this solution on YOUR website!2 x + 3 y = 200 .............1 5 x + 4 y = 290 .............2 Eliminate y multiply (1)by -4 Multiply (2) by 3 -8 x -12 y = -800 15 x + 12 y = 870 Add the two equations 7 x = 70 / 7 x = 10 plug value of x in (1) 2 x + 3 y = 200 20 + 3 y = 200 3 y = 200 -20 3 y = 180 y = 60 x= 10 y= 60 m.ananth@hotmail.ca
 Sequences-and-series/683555: A ball takes 1 second to hit the ground when dropped.It then takes 90%of this time to rebound to its new height and this continues until the ball comes to rest.What is the geometric sequence?1 solutions Answer 423612 by mananth(12270)   on 2012-11-21 03:18:26 (Show Source): You can put this solution on YOUR website!To fall down it takes 1second s. To go up on rebound 0.9 s (90% of the time) To fall down 0.9 s (When it falls down t=,no change in time) To go up and rebound II 0.9*0.9 = 0.9^2 To fall down 0.9^2 To go up 0.9^3 To come down 0.9^3 Hence the time taken is 1 + 2(0.9) + 2(0.9) ^2 + 2(0.9) ^3 +...
 Money_Word_Problems/683103: Melody has \$45,000 to invest and wishes to receive an annual income of \$4290 from this money. She has chosen investments that pay 5%, 8%, and 12% simple interest. Melody wants to have the amount invested at 12% to be double the amount invested at 8%. How much should she invest at each rate?1 solutions Answer 423472 by mananth(12270)   on 2012-11-20 01:03:24 (Show Source): You can put this solution on YOUR website!Total money \$45,000 annual income of \$4290 from this money. 5%,(45000-3x) 8%,,----------------x and 12% ------------2x (double of x) equate the interest (45000-3x)*5% +8%x+12%(2x)=4290 multiply by 100 (45000-3x)*5 +8x+12(2x)=4290*100 225000-15x+8x+24x=429000 17x= 429000-225000 17x=204000 /17 x=204000/17 x=12000 nvestment @ 8% Now you can calculate the other amounts
 Linear-equations/683119: a part of monthly expenses of a family on milk is fixed which is rs. 500 and the remaining varies with the quality of milk taken extra at the rate of rs.20 per kg. taking the quantity of milk required as x kg and the total expenditure on milk is y write a linear equation for this information and draw the graph 1 solutions Answer 423471 by mananth(12270)   on 2012-11-20 00:46:41 (Show Source): You can put this solution on YOUR website!milk bought = x kg total expediture = y Fixed amount = Rs500 variable is x y= 500+20x generate values of x & y when x= 10, y= 700 x=20, y=900 x=50,y=1500
 Travel_Word_Problems/683004: A crew of four practices rowing up a river, then back down for the same distance. The current of the river is 3 km/hr. Currently the crew can can row at 15 km/hr in still water and makes the round trip in 25 minutes. How far upstream did they row?1 solutions Answer 423428 by mananth(12270)   on 2012-11-19 20:04:44 (Show Source): You can put this solution on YOUR website!Let distance be x upstream speed = 15-3=12 mi/h downstream speed = 15+3=18 mi/h Time upstream + time downstream = 25 minutes= 25/60 = 5/12 hours t=d/r x/12 + x/18 = 5/12 LCD = 36 multiply equation by 36 3x+2x=15 5x=15 x=3 miles
 Trigonometry-basics/682943: I need help slove this identity, please show the steps becasue I subed in 2 for B and both sides were the same so I know it is an identity but I do not how to prove it without subing in a number (1+2inBcosB)/(sinB+cosB)=sinB+cosB Thanks :)1 solutions Answer 423426 by mananth(12270)   on 2012-11-19 19:57:08 (Show Source): You can put this solution on YOUR website! = sinB+cosB
 Polynomials-and-rational-expressions/682986: factor 36a^5b^5+9ab^3-72ab^51 solutions Answer 423419 by mananth(12270)   on 2012-11-19 19:46:19 (Show Source):
 Surface-area/682987: If the ratio of two areas of circle A+B is 4, what is the ratio of teh radii of A+B1 solutions Answer 423418 by mananth(12270)   on 2012-11-19 19:43:18 (Show Source): You can put this solution on YOUR website!Area of circle A = pi*r1^2 Area of circle B = pi*r2^2 Area of circle A = pi*r1^2 ---------------- ------- Area of circle B = pi*r2^2 4= r1^2/r2^2 r1/r2 = sqrt(4) r1/r2= 2 (the positive value )
 Functions/682979: Find the equation in slope-intercept form of the line satisfying the conditions through (4,5); m=-5/91 solutions Answer 423417 by mananth(12270)   on 2012-11-19 19:40:12 (Show Source): You can put this solution on YOUR website!point (4,5) m=-5/9 The equation of line in point slope form is where (x1,y1) is (4,5) and m= -5/9 y-5= (-5/9) (x-4) multiply equation by 9 to eliminate the denominator 9(y-5)=(-5)(x-4) 9y-45=-5x+20 9y=-5x+20+45 9y=-5x+45 /9 y=(-5/9)x+5
 Numeric_Fractions/682970: how do you solve (in detail- understanding) this 6 grade math problem... 4 1/5 -1 1/2 1 solutions Answer 423414 by mananth(12270)   on 2012-11-19 19:33:54 (Show Source): You can put this solution on YOUR website! convert the mixed fraction into a simple fraction We have to equalize the denominator to enable us to add or subtract the numerators of the two fractions. the denominators of the fractions are 5 &2 multiply both of them we get 10 This will be the common denominator 5 times 2 is 10 so multiply the numerator and denominator of first fraction by 2 2 times 5 is 10 & multiply and divide the second fraction by 5 to get 10 denominator Since the denominators are same we can subtract the numerators. There you are!
 Trigonometry-basics/682967: what is the x and y intercept of 2x plus 8y=-241 solutions Answer 423408 by mananth(12270)   on 2012-11-19 19:19:07 (Show Source): You can put this solution on YOUR website!2x+8y=-24 For X intercept plug y=0 2x+0=-24 2x=-24 /2 x=-12 For Y intercept plug x =0 0+8y=-24 8y=-24 /-8 y=-3
 Money_Word_Problems/682570: An investor invested a total of \$900 in two mutual funds. One fund earned a 8% profit while the other earned a 2% profit. If the investor's total profit was \$48, how much was invested in each mutual fund?1 solutions Answer 423250 by mananth(12270)   on 2012-11-19 01:10:23 (Show Source): You can put this solution on YOUR website!Part I 8.00% per annum ------------- Amount invested =x Part II 2.00% per annum ------------ Amount invested = y = 900 Interest----- 48 Part I 8.00% per annum ---x Part II 2.00% per annum ---y Total investment x + 1 y= 900 -------------1 Interest on both investments 8.00% x + 2.00% y= 48 Multiply by 100 8 x + 2 y= 4800.00 --------2 Multiply (1) by -8 we get -8 x -8 y= -7200.00 Add this to (2) 0 x -6 y= -2400 divide by -6 y = 400 Part I 8.00% \$ 500 Part II 2.00% \$ 400 CHECK 500 --------- 8.00% ------- 40.00 400 ------------- 2.00% ------- 8.00 Total -------------------- 48.00 m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/682569: Arasoo is 4 years older than Peter.Ali is 2 years younger than Peter.If the sum of their ages is 47,what are their respective ages?1 solutions Answer 423249 by mananth(12270)   on 2012-11-19 01:07:25 (Show Source): You can put this solution on YOUR website!Let Peter's age be x years Arasoo's age = x+4 ali's age x-2 years Their sum = 47 years x+x+4+x-2=47 3x=45 x=15 Peter's age = 15 Arasoo's age = x+4 , =19 years Ali's age = x-2 . = 13 years
 Travel_Word_Problems/682567: A boeing 747 flies the 3000 mile distance from Los Angeles to NEw York, with the tailwind, in 5 hours. The return trip, against the wind, takes 6 hours. Find the speed of the plane and the speed of the wind.1 solutions Answer 423248 by mananth(12270)   on 2012-11-19 01:03:17 (Show Source): You can put this solution on YOUR website!Find boat speed & current speed Both times given Plane speed =x mph wind speed =y mph against wind 6 hours with wind 5 hours Distance against 3000 miles distance with wind 3000 miles t=d/r against wind - 3000 / ( x - y )= 6 6(x-y)=3000 6x-6y= 3000 ....................1 3000/(x-y)= 5 5(x+y) =3000 5x+5y =3000 ...............2 Multiply (1) by 5 Multiply (2) by 6 we get y 30 x + -30 y = 15000 30 x + 30 = 18000 60 x = 33000 / 60 x = 550 mph plug value of x in (1) y 6 x -6 y = 3000 3300 -6 -3300 = 3000 -6 y = 3000 -6 y = -300 mph y = 50 Plane speed 550 mph wind speed 50 mph m.ananth@hotmail.ca
 Proportions/682565: A metallurgist needs to produce 10kg of an alloy which is 65% copper and 35% tin. He has an alloy which is 50% copper and 50% tin. How Much of this 50-50 alloy must he melt together with pure copper to make the desired alloy? How much copper must he use? If necessary, round each answer to the nearest tenth of a a kilogram.1 solutions Answer 423247 by mananth(12270)   on 2012-11-19 00:58:44 (Show Source): You can put this solution on YOUR website!Copper percent ---------------- quantity Metal alloy I 50 ---------------- x Kg Pure copper 100 ------ 10 - x Kg Mixture 65 ---------------- 10 600 50x+100 (10-x) =65*10 5000x+10000(10 -x)=65000 5000x+ 100000 -10000x = 65000 5000x - 10000 x = 65000 - -100000 -5000 x = -35000 / -5000 x = 7 Kg 50.00% Metal alloy I 3 Kg 100.00% Pure copper m.ananth@hotmail.ca
 Exponential-and-logarithmic-functions/682451: Please help. I need to solve this equation for t and I have no clue on how to do it. If you could please show the steps I would appreciate it very much. (a)/(1+be^-kt)= (a/2) This equation is asking for the time t at which the population size will be equal to half of its maximum (a/2). I need to solve for t.1 solutions Answer 423186 by mananth(12270)   on 2012-11-18 20:32:29 (Show Source):
 Complex_Numbers/682454: How would I solve 5√3 over 3√5?1 solutions Answer 423184 by mananth(12270)   on 2012-11-18 20:17:49 (Show Source): You can put this solution on YOUR website! multiply by the conjugate
 Quadratic_Equations/682430: Bill can row 3 mph in still water. It takes him 3 hr 36 min to go 3 mi upstream and then return. Find the speed of the current.1 solutions Answer 423183 by mananth(12270)   on 2012-11-18 20:13:31 (Show Source): You can put this solution on YOUR website!Rowing speed = 3 mph current speed = x mph against current = 3 - x with current = 3 + x Total distance =3 miles Total Time= 3.60 hours Time upstream + time downstream = 3/(3-x)+3/(3+x )=3.6 3(3+x)+ 3(3-x)= 3.60(9- 1X^2) 9+3x+ 9-3x=32.4-3.6 X^2 18 - -32.4 = -3.6 X^2 -14.4 =-3.6 x^2 -3.6 x^2= -14.4 x^2 = 4 X = +/- 2 Ignore negative value current speed = 2mph
 Linear-systems/682433: Use the elimination method to solve the system of equations. a+9b=23 a+2b=2 1 solutions Answer 423176 by mananth(12270)   on 2012-11-18 19:43:40 (Show Source): You can put this solution on YOUR website!1 a + 9 b = 23 .............1 1 a + 2 b = 2 .............2 Eliminate y multiply (1)by -2 Multiply (2) by 9 -2 a -18 b = -46 9 a + 18 b = 18 Add the two equations 7 a = -28 / 7 a = -4 plug value of a in (1) 1 a + 9 b = 23 -4 + 9 b = 23 9 b = 23 + 4 9 b = 27 b = 3 x= -4 y= 3 m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/682064: Need help putting this world problem into a linear equation: There are three types of phones in a shipment: Android, Blackberry, and iphone. The shipment has the following specifications: - The total number of phones is 195. - The total value is \$88225. - The number of iphones equals twice the number of Android phones and twice the number of Blackberry phones combined. - The value of each phone is \$195 for an Android, \$150 for a Blackberry, and \$595 for an iphone1 solutions Answer 423032 by mananth(12270)   on 2012-11-18 00:06:19 (Show Source): You can put this solution on YOUR website! Android,...........x Blackberry,........y and iphone.--------z The total number of phones is 195. x+y+z=195..................(1) - The total value is \$88225. The value of each phone is \$195 for an Android, \$150 for a Blackberry, and \$595 for an iphone 195x+150y+595z=88225.............(2) - The number of iphones equals twice the number of Android phones and twice the number of Blackberry phones combined. z=2x+2y 2x+2y-z=0.....................(3) solve for x y & z You will get 25, 40,130 phones respectively. m.ananth@hotmail.com
 Complex_Numbers/681954: {(125y3 + 216)/(64y3 - 1)}/{(25y2-36)/(16y2+4y+1)}1 solutions Answer 423002 by mananth(12270)   on 2012-11-17 21:23:33 (Show Source): You can put this solution on YOUR website! / / Cancel of the common factors
 Travel_Word_Problems/682040: a rowing team rowing with the current, traveled 40km in 2 hrs. rowing against the current the team can only travel 16 km in 2 hrs find the team rowing rate in calm water and the rate of the current1 solutions Answer 422997 by mananth(12270)   on 2012-11-17 20:48:07 (Show Source): You can put this solution on YOUR website!Rowing speed =x mph current speed =y mph against current 2 hours with current 2 hours Distance with current 40 miles distance against current 16 t=d/r against current (x-y) 16.00 / ( x - y )= 2.00 2.00 x - -2.00 y = 16.00 ....................1 with current (x+y) 40.00 / ( x + y )= 2.00 2.00 ( x + y ) = 40.00 2.00 x + 2.00 y = 40.00 ...............2 Multiply (1) by 1.00 Multiply (2) by 1.00 we get y 2.00 x + -2.00 y = 16.00 2.00 x + 2.00 = 40.00 4.00 x = 56.00 / 4.00 x = 14 mph plug value of x in (1) y 2 x -2 y = 16 28 -2 -28 = 16 -2 y = 16 -2 y = -12 mph y = 6 Rowing 14 mph current 6 mph
 Travel_Word_Problems/681980: I live 260 miles from a popular mountain retreat. On my way there to do some mountain biking, my car had a break down forcing me to bike the rest of the way. If I drove 2 hours longer than I biked and average 60 mph driving and 10 mph biking, how many hours did I spend biking to the resort?1 solutions Answer 422991 by mananth(12270)   on 2012-11-17 20:41:58 (Show Source): You can put this solution on YOUR website!let biking distance be x biking speed = 10 mph driving distance = 260-x driving speed = 60 mph x/10 +2=(260-x)/60 x/10 -(260-x)/60 = -2 LCD = 60 multiply equation by 60 6x-260+x=-2*60 7x= -120+260 7x=140 /7 x= 20 miles time biking = distance biking/speed biking =20/10 = 2 hours
 Travel_Word_Problems/682028: carlos and sheri drove a total of 258 miles in 5 hours. carlos drove the first part of the trip and averaged 53 miles per hour. sheri drove the remander of the trip and averaged 51 miles per hour. for approximately how many hours did sheri drive?1 solutions Answer 422988 by mananth(12270)   on 2012-11-17 20:29:02 (Show Source): You can put this solution on YOUR website!let carlos drive x miles speed carlos = 53mi/h sheri drives 258-x miles speed sheri 51 mi/h Time carlos drove + time cheri drove = 5 hours t=d/r x/53 + (258-x)/51 = 5 LCD = (53)*(51) 51x+13674-53x=5*51*53 -2x=-13674+13515 -2x=-159 /-2 x=79.5 miles Sheri drove for 258-79.5 =178.5 t=d/r sheri drove for 178.5/51 = 3.5 hours
 �t�e�s�t/681833: find the leangth of the line segment joining the following pairs of points: (a,0)and(0,b)1 solutions Answer 422820 by mananth(12270)   on 2012-11-17 00:36:10 (Show Source): You can put this solution on YOUR website!Distance between two points x1 y1 x2 y2 a 0 0 b d= d= d=
 Mixture_Word_Problems/681777: If an object is projected vertically upward from an altitude of a feet with an initial velocity of v ft/sec, then its distance s(t) above the ground after t seconds is s(t) = −16t2 + vt + a. If s(1) = 99 and s(4) = 129, what are v and a? 1 solutions Answer 422783 by mananth(12270)   on 2012-11-16 20:18:07 (Show Source): You can put this solution on YOUR website!s(t) = −16t2 + vt + a. If s(1) = 99 and s(4) = 129, what are v and a? 99= -16(1)^2+v(1)+a 99=v+a-16 v+a=99+16 v+a=115..........(1) 129= -16(4^2)+4v+a 129=-256+4v+a 4v+a=129+256 4v+a=386...........(2) Solve (1) & (2) subtract (2) from (1) -3v=-276 v=92 Plug v in equation above to get a
 Problems-with-consecutive-odd-even-integers/681778: The product of two consecutive even integers is 12 less than 6 times their sum.1 solutions Answer 422779 by mananth(12270)   on 2012-11-16 20:07:08 (Show Source): You can put this solution on YOUR website!let the integerrs be x & x+2 Product = x(x+2) 12 less than 6 times the sum 6(x+x+2)-12 6(2x+2)-12 x(x+2)=6(2x+2)-12 x^2+2x=12x+12-12 x^2+2x-12x=0 x^2-10x=0 x(x-10)=0 x=0 OR 10 10,12