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# Recent problems solved by 'mananth'

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 Radicals/378083: 12 - 3√17 / 4 - √171 solutions Answer 268604 by mananth(12270)   on 2010-11-30 00:48:45 (Show Source): You can put this solution on YOUR website! ... multiply by .. ... ... ... -3/-1 = 3 ... m.ananth@hotmail.ca
 Radicals/378085: Simplify. 12 - 3√17 / 4 - √171 solutions Answer 268603 by mananth(12270)   on 2010-11-30 00:41:17 (Show Source): You can put this solution on YOUR website! ... multiply by .. ... ... ... -3/-1 = 3 ... m.ananth@hotmail.ca
 Percentage-and-ratio-word-problems/378080: at an iceskating performance, there are 2/5 as many adults as children. among the children, the ratio of school children to non school children toddlers is 7:1. find the number of non school children toddlers if the total number of people in the audience is 28001 solutions Answer 268602 by mananth(12270)   on 2010-11-30 00:26:51 (Show Source): You can put this solution on YOUR website!at an iceskating performance, there are 2/5 as many adults as children. among the children, the ratio of school children to non school children toddlers is 7:1. find the number of non school children toddlers if the total number of people in the audience is 2800 ... non school children toddlers be x school cildren will be 7x .. Total children = 7x+x=8x .. Adult = (2/5) * 8x .. 8x + 16x/5 = 2800 multiply by 5 8x*5 + 16x/5 *5 = 2800*5 40x+16x= 14000 56x=14000 /56 x= 14000/56 x = 250 non school children toddlers school children = 7x = 1750 adult = 2/5 * 2000 =800 adult 800, school children = 1750, nonschool children toddlers = 250 ... m.ananth@hotmail.ca
 Money_Word_Problems/378064: a cashier has 20 bills, all of which are \$10 or \$20 bills. The total value of the money is \$330. How many of each type does the cashier have?1 solutions Answer 268598 by mananth(12270)   on 2010-11-29 23:19:43 (Show Source): You can put this solution on YOUR website!\$10 bill -------x \$20 bill -------y ... x+y=20......................1 ... 10+20y=330 /10 x+2y=33.....................2 multiply equation 1 by -1 -x-y-20 add this to (2) -x+x-y+2y=-20+33 y = 13 \$ 20 bills x= 7 \$10 bills ... m.ananth@hotmail.ca
 Evaluation_Word_Problems/378053: at white plains bowl the charge per game is \$2.50 and it costs \$2.00 for shoe rental. at homefield bowl the cost is \$2.00 per game and the shoe rental is \$4.00. they are wondering for how many games will the cost to bowl be the same at both places. use elimination to solve.1 solutions Answer 268596 by mananth(12270)   on 2010-11-29 23:16:13 (Show Source): You can put this solution on YOUR website!Let the number of games played be x White plain bowl 2+2.50x is the cost Home field 4 + 2x .. equate them to find the games 2+2.50x = 4+2x -2x 2+2.50x-2x=4 -2 2.50x-2x=4-2 0.5x=2 /0.5 x=2/0.5 x= 4 games their costs are equal ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/378062: what is 2x squared minus x minus 151 solutions Answer 268594 by mananth(12270)   on 2010-11-29 23:10:40 (Show Source): You can put this solution on YOUR website!2x^2-x-15 2x^2-6x+5x-15 2x(x-3)+5(x-3) (x-3)(2x+5) ... m.ananth@hotmail.ca
 Linear-systems/378058: A man is nine times as old as his son. In nine years, he will be only three times as old as his son. How old are each now? Solve using elimination method.1 solutions Answer 268591 by mananth(12270)   on 2010-11-29 23:08:15 (Show Source): You can put this solution on YOUR website!let son be x years father = y ... y=9x after 3 years son = x+9 father = y+9 (y+9)=3(x+9) plug value of y =9x (9x+9)=3x+27 9x+9=3x+27 -3x 9x-3x+9=27 6x+9=27 -9 6x=18 /6 x=3 son's age now father's age = 9x = 27 years now .. m.ananth@hotmail.ca
 Problems-with-consecutive-odd-even-integers/378034: Find all sets of three consecutive odd integers whose sum is at least 47 less than 4 times the third integer. Please help! Thank you. 1 solutions Answer 268588 by mananth(12270)   on 2010-11-29 22:59:21 (Show Source): You can put this solution on YOUR website!let x, x+2, x+4 be the integers. their sum = x+x+2+x+4 =3x+6 ... 47 less than 4 times the third integer = 4(x+4)-47 ... 3x+6 <= 4(x+4)-47 3x+6<=4x+16-47 3x+6<=4x-31 -6 3x+6-6 <=4x-31-6 3x<=4x-37 -4x 3x-4x<=4x-4x-37 -x<=-37 /-1 x>=37 37,39,41,is the first set ... m.ananth@hotmail.ca
 Geometry_Word_Problems/377912: The longer leg of a right triangle is 6 less than 3 times the shorter leg. If the hypotenuse is 26cm., find the length of the two legs. Define the variables, set up your equation and solve.1 solutions Answer 268532 by mananth(12270)   on 2010-11-29 20:31:42 (Show Source): You can put this solution on YOUR website!let shorter leg be x longer leg = 3x-6 hypotenuse = 26 cm ... Pythagoras theorem x^2+(3x-6)^2= 26^2 x^2+9x^2-36x+36=26^2 10x^2-36x+36-676=0 10x^2-36x-640=0 10x^2-100x+64x-640=0 10x(x-10)+64(x-10)=0 (10x+64)(x-10)=0 c= 10 which is positive one leg is 10 cm the other leg = 3x-6 = 30-6 =24cm .. m.ananth@hotmail.ca
 Quadratic_Equations/377910: x^2 + 8x + 12= 01 solutions Answer 268511 by mananth(12270)   on 2010-11-29 20:08:27 (Show Source): You can put this solution on YOUR website!x^2 + 8x + 12= 0 ... x^2+6x+2x+12 x(x+6)+2(x+6)=0 (x+6)(x+2)=0 x=-6, x=-2 .. m.ananth@hotmail.ca
 Complex_Numbers/377901: The sum of three numbers is 18. The sum of the first and second number is 15, and the first number is 3 times the third number. Find the numbers1 solutions Answer 268505 by mananth(12270)   on 2010-11-29 20:04:40 (Show Source): You can put this solution on YOUR website!let the numbers be x , y , z .. x+y+z=18...........1 x+y =15............2 x= 3z..............3 ... x+y =15 plug in (1) 15+z= 18 -15 ... x=3z .. x+y+z=18 9+3+y=18 12+y=18 -12 y = 18-12 . .. numbers are 9, 6, 3 ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/377891: Use the system of equations to solve the following: The sum of two numbers is 73. When the smaller number is subtracted from twice the greater number the result is 50. Find the numbers.1 solutions Answer 268497 by mananth(12270)   on 2010-11-29 19:56:04 (Show Source): You can put this solution on YOUR website!let smaller number be x the other number be y x+y=73.........................1 2y-x=50........................2 Add the equations 3y=123 /3 y = 123/3 y=41.. plug value of y in (1) x+41=73 -41 x=73-41 x=32 ... x=32, y =41 ... m.ananth@hotmail.ca
 Equations/377883: Problem : 7+w - 10 = 2w Question : What is w ?1 solutions Answer 268490 by mananth(12270)   on 2010-11-29 19:49:22 (Show Source): You can put this solution on YOUR website!7+w - 10 = 2w 7-10+w=2w -3+w=2w add 3 to both sides -3+3+w=2w+3 w=2w+3 add -2w to both sides w-2w=-2w+2w+3 -w=+3 /-1 w=-3 ... m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/377863: In 1920 a record for a race was 45.3 seconds. In 1940 it was 44.7 seconds. R(t)= the Records of the race and let t = the number of years since 1920. 1.Find a linear function that fits the Data 2. Use the function to predict the race 2003, and 2006 3. Find the year when the record will be 42.5 seconds. 1 solutions Answer 268486 by mananth(12270)   on 2010-11-29 19:45:51 (Show Source): You can put this solution on YOUR website!In 1920 a record for a race was 45.3 seconds. In 1940 it was 44.7 seconds. decrease per year = (45.3-44.7) /20 =0.6/20 =0.03 per year. R(t) = 45.3-0.03t ...... In 2003 ------------- R(83)= 45.5-0.03*83 R(83)=45.5 -2.49 R(83)=42.81 In 2003 the record will be 42.81 seconds. plug t=86 for 2006 .. 3.) 42.5 = 45.5 -0.03t 0.03t=45.5-42.5 0.03 t = 3 t = 3/0.03 t=100 Add 100 years to 1920= 2020 In 2020 the recoed will be 42.5 seconds m.ananth@hotmail.ca
 Linear-systems/377860: I need to write an equation in standard form of the line that passes through the given point and has the given slope. (4,3),m=7 1 solutions Answer 268473 by mananth(12270)   on 2010-11-29 19:28:03 (Show Source): You can put this solution on YOUR website!(4,3),m=7 .. y= mx +b plug value of x,y & m .. 3=7*4+b 3=28+b -28 b=-25 .. y= mx +b m=7, b= -25 y = 7x-25 is the equation. m.ananth@hotmail.ca
 Expressions-with-variables/377853: Solve using the multiplication principle first. Then use the elimination method. 2x+y=13 4x+2y=23 I'm not sure if I multiply equation #1 by -2 to eliminate x? If I do that, then I eliminate y. I'm confused, what do I multiply? Thank you.1 solutions Answer 268469 by mananth(12270)   on 2010-11-29 19:23:03 (Show Source): You can put this solution on YOUR website!2x+y=13 4x+2y=23 multiply the first equation by -2 -4x-2y=-26 add to second -4x+4x+2y-2y=23-26 0=-3 ... This system has no solution. They are parallel lines Just have a look at the graphs ... m.annath@hotmail.ca
 Angles/377840: Hi okay, I dont understand the question "if two angles are complementary and the larger angle is 5 less than 3 times the smaller, then find these two angle measurements. Draw and Label a sketch to help you" I drew a sketch and labeled it but it did not help me, I still dont get it! Please Help Me! Thanks very much!1 solutions Answer 268465 by mananth(12270)   on 2010-11-29 19:16:22 (Show Source): You can put this solution on YOUR website!let the angle be x the complementary will be 90 -x .. x= 3(90-x)-5 x= 270-3x-5 x=265-3x add 3x x+3x=265-3x+3x 4x=265 x=66.5 deg.one angle .. 90-66.5 = 23.5 deg is the other angle .. m.ananth@hotmail.ca
 Linear-systems/377513: suppose that y varies directly as the sqaure root of x, and that y=32 when x=16. What is y when x=50?1 solutions Answer 268242 by mananth(12270)   on 2010-11-29 09:29:24 (Show Source): You can put this solution on YOUR website!suppose that y varies directly as the sqaure root of x, and that y=32 when x=16. What is y when x=50? ... ... .. x=16,y=32 plug the value ... ... 32=4k /4 k=32/4 k=8 ... x=50, k= 8 y =56.56 ... m.ananth@hotmail.ca
 Mixture_Word_Problems/377481: Lara, a pharmacist, has 60 mL of an 8% alcohol solution. How Much water should be evaporated so that the solution that remains is 10% alcohol?1 solutions Answer 268218 by mananth(12270)   on 2010-11-29 05:51:18 (Show Source): You can put this solution on YOUR website!let water evaporated be x ml ... acid 8% ------60 ml ... final quantity = 10% ----(60-x) .. 60*8 = 10(60-x) 480=600-10x 10x=600-480 10x= 120 /10 x=12 ml should be evaporated. ... m.ananth@hotmail.ca
 Mixture_Word_Problems/377480: A big barrel contains 300 L of a 6% solution of lawn fertilizer. How much water should be added to obtain a 5% solution?1 solutions Answer 268217 by mananth(12270)   on 2010-11-29 05:46:31 (Show Source): You can put this solution on YOUR website!Acid 6 % ----------300 L water 0% ---------- x L required 5% ------ Total will be x+300 .. 6*300+0*x=5(x+300) 1800 =5x+1500 -1500 1800-1500=5x 300 =5x /5 300/5 = x 60 = x 60 liters of water ... m.ananth@hotmail.ca
 Rate-of-work-word-problems/377477: JV can edit 15 essays in 10 hours. Ayah needs 15 hours to do the same job. If they work together, how long will it take them to edit the essays.1 solutions Answer 268214 by mananth(12270)   on 2010-11-29 05:34:47 (Show Source): You can put this solution on YOUR website!JV can edit 15 essays in 10 hours. Ayah needs 15 hours to do the same job. If they work together, how long will it take them to edit the essays. .. JV .......... 10 hours JV does 1/10 of the job in 1 hour Ayah ..........15 hours Ayah does 1/15 of the job in 1 hour ... Together they do job in 1 hour LCD = 30 = = = of the job in 1 hour so together they take 6 hours to do the editing ... m.ananth@hotmail.ca
 Travel_Word_Problems/377476: Jana can jog 5 miles downhill in the same time that it takes her to jog 3 miles uphill. Find her jogging rate for each way if she jogs downhill 4 mi/h faster than she jogs uphill.1 solutions Answer 268212 by mananth(12270)   on 2010-11-29 05:29:01 (Show Source): You can put this solution on YOUR website!uphill speed = x downhill speed = x+4 .. time uphill = time downhill .. cross multiply 3(x+4)=5x 3x+12=5x 5x-3x=12 2x=12 /2 x= 6 mph. up hill speed downhill speed = 10 mph ... m.ananth@hotmail.ca
 Numeric_Fractions/377380: Given the formula, solve for the indicated variable. A = P(1 + nr) for r1 solutions Answer 268210 by mananth(12270)   on 2010-11-29 05:25:00 (Show Source): You can put this solution on YOUR website!A = P(1 + nr) for r ... divide by p } .. Add -1 ... divide by n ... ... m.ananth@hotmail.ca
 Travel_Word_Problems/377396: 2800 km trip New plane flies 100 km faster Trip time reduced 30 minutes What is speed of new plane?1 solutions Answer 268208 by mananth(12270)   on 2010-11-29 05:13:38 (Show Source): You can put this solution on YOUR website!distance = 2800 km let speed of plane be x time taken = 2800/x ... New plane speed = x+100 time= 2800/(x+100) 2800/x - 2800/(x+100)= 1/2 .. LCD = x(x+100) ( cross multiply .. 2(2800x+280000-2800x)=x(x+100) 2*280,000=x^2+100x x^2+100x-560,000 =0 x^2+800x-700x-560,000=0 x(x+800)-700(x+800)=0 (x+800)(x-700)=0 x=-800 OR x= 700 .. The speed of new plane = 700+100 = 800 kmph ... m.ananth@hotmail.ca
 Human-and-algebraic-language/377431: The neighborhood children have been cutting diagonally across her lawn instead of walking around the yard. If the diagonally distance across the lawn is 30 feet and the longer part of the sidewalk is twice the shorter lenght, how many feet, are the children saving by cutting across the lawn?1 solutions Answer 268204 by mananth(12270)   on 2010-11-29 04:57:06 (Show Source): You can put this solution on YOUR website!The neighborhood children have been cutting diagonally across her lawn instead of walking around the yard. If the diagonally distance across the lawn is 30 feet and the longer part of the sidewalk is twice the shorter lenght, how many feet, are the children saving by cutting across the lawn? ... diagonal = 30 feet .. on side = x other side 2x ... right triangle x^2+(2x)^2=30^2 x^2+4x^2= 900 5x^2=900 /5 x^2= 180 .. x= +/- sqrt(180) x= +13.4 feet one side other side = 2* 13.4 = 26 .8 feet ... sum of sides = 13.4 +26.8 = 40.2 feet hypotenuse = 30 difference = 40.2-30=10.2 feet is waht they save. ... m.ananth@hotmail.ca
 Equations/377465: if y is directly proportional to x, and y = 34 when x = -2, what is y when x = 5?1 solutions Answer 268201 by mananth(12270)   on 2010-11-29 04:47:31 (Show Source): You can put this solution on YOUR website! y=kx k = constant. ... x=-2, y =34 34= k*-2 34=-2k /-2 k=-17.. .............. y= -17x x=5 y= 5 * (-17) y =-85 ... m.ananth@hotmail.ca
 Miscellaneous_Word_Problems/377474: Two pipes fill the storage tank in 20 min. with both faucets running. If the cold-water faucet runs as fast as the hot water, how long would it take the cold-water faucet to fill the tub by itself? I really need help in answering this..1 solutions Answer 268200 by mananth(12270)   on 2010-11-29 04:42:51 (Show Source): You can put this solution on YOUR website!Practically if you visualise properly you will infer that it will take 40 minutes. double the time since both rates are equal. ... let each fill in x minutes .. each one does 1/x of the job in 1 minute. togther they do 1/20 of the job in 1 minute 1/x +1/x = 1/20 .. LCD = x (1+1)/x = 1/20 2/x= 1/20 cross multiply 2*20 = 1*x 40 = x each will fillin 40 minutes. ... m.ananth@hotmail.ca
 Inequalities/377437: A cell phone company has offered you two different rates. The first rate is \$35 per month and 5 cents per phone call (time does not matter). The second offer is \$55 per month and 2 cents per call. Set up the inequality to model this problem and find where it is less expensive to go with the second plan.1 solutions Answer 268176 by mananth(12270)   on 2010-11-29 02:08:03 (Show Source): You can put this solution on YOUR website!A cell phone company has offered you two different rates. The first rate is \$35 per month and 5 cents per phone call (time does not matter). The second offer is \$55 per month and 2 cents per call. Set up the inequality to model this problem and find where it is less expensive to go with the second plan. ... Plan A let x be number of calls made per mont 35+0.05x < 55+0.02x -35 0.05x<55-35+0.02x -0.02x 0.05x-0.02x<20 0.03x <20 /0.03 x<20/0.03 x<666.6 calls .. when the calls are less than 666 Plan A is better deal.
 Age_Word_Problems/377444: Dalton's age is half of Chen's. In 10 years Chen's age will be three times what Dalton's was 5 years ago. What are their ages?1 solutions Answer 268168 by mananth(12270)   on 2010-11-29 01:05:14 (Show Source): You can put this solution on YOUR website!Dalton's age is half of Chen's. In 10 years Chen's age will be three times what Dalton's was 5 years ago. What are their ages? ... let Chen's age be x Dalton's age = x/2 .. after 10 years chen's age = x+10 Dalton's age = (x/2) +10 .. five years ago Dalton was (x/2)-5 years .. x+10= 3((x/2)-5) x+10=3(x-10)/2 x+10=3x-30/2 multiply by 2 2(x+10)=3x-30 2x+20=3x-30 2x-3x=-50 -x=-50 x= 50 chen's age Dalton's age = x/2 = 25 years ... m.ananth@hotmail.ca
 Exponential-and-logarithmic-functions/377449: The question says that one square metre measures 1m by 1m It then asks for you to write 1m^2 in square millinetres as a product of powers and as a single power. For the product of powers part, I wrote down 1^1 x 1^1= 1^2.1 solutions Answer 268166 by mananth(12270)   on 2010-11-29 00:36:42 (Show Source): You can put this solution on YOUR website!1meter = 1000 mm = 10^3mm .. L*W = Area sq. mm ... m.ananth@hotmail.ca
 Triangles/377446: One Leg Of A Right Triangle Is 21 Inches Longer Than The Smaller Leg, And The Hypotenuse Is 24 Inches Longer Than The Smaller Leg. Find The Lengths Of The Sides Of The Triangle.1 solutions Answer 268165 by mananth(12270)   on 2010-11-29 00:32:07 (Show Source): You can put this solution on YOUR website!One Leg Of A Right Triangle Is 21 Inches Longer Than The Smaller Leg, And The Hypotenuse Is 24 Inches Longer Than The Smaller Leg. Find The Lengths Of The Sides Of The Triangle. ... smaller leg = x longre leg = x+21 hypotenuse = x+24 ... Hyp^2 = leg1^2 + leg2^2 .. (x+24)^2=(x+21)^2+x^2 x^2+48x+576=x^2+42x+441+x^2 re write the equation x^2+x^2-x^2-48x+42x-576+441=0 x^2-6x-135=0 x^2-15x+9x-135=0 x(x-15)+9(x-15)=0 (x-15)(x+9)=0 x= 15 ignore -9 ... The sides are 15, 36,39 inches ... m.ananth@hotmail.ca