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 Expressions-with-variables/206147: 1. The denominator of a fraction is 12 more than the numerator. If 16 is added to the numerator and 16 is subtracted from the denominator, the value of the resulting fraction is equal to 2/1. Find the original fraction. 2. A number is 6 times the sum of its digits. The tens digit is 1 greater than the units digit. Find the number.1 solutions Answer 155698 by ankor@dixie-net.com(16526)   on 2009-08-10 13:38:23 (Show Source): You can put this solution on YOUR website!1. The denominator of a fraction is 12 more than the numerator. If 16 is added to the numerator and 16 is subtracted from the denominator, the value of the resulting fraction is equal to 2/1. Find the original fraction. ; Let x = the numerator then (x+12) = the denominator : 2/1 is just 2 : = 2 which is = 2 : x + 16 = 2(x-4) : x + 16 = 2x - 8 : 16 + 8 = 2x - x : 24 = x : The original fraction = : is this true? = = 2 : : 2. A number is 6 times the sum of its digits. The tens digit is 1 greater than the units digit. Find the number. : Let x = the 10's digit; let y = the units : 10x + y = "the two digit number" ; 10x + y = 6(x + y) 10x + y = 6x + 6y 10x - 6x = 6y - y 4x = 5y : The 10's digit is 1 greater than the units x = y + 1 : replace x with y+1 4(y+1) = 5y 4y + 4 = 5y 4 = 5y - 4y y = 4 then 54 is the number : : Is this true: 54 = 6(5+4)
 Quadratic_Equations/206100: 20. A punter can kick a football with an initial velocity of 48 feet per second. How many seconds will it take for the ball to return to the ground? (Hint: use the formula h= vt – 16t2.)1 solutions Answer 155686 by ankor@dixie-net.com(16526)   on 2009-08-10 12:25:12 (Show Source): You can put this solution on YOUR website!0. A punter can kick a football with an initial velocity of 48 feet per second. How many seconds will it take for the ball to return to the ground? (Hint: use the formula h= vt – 16t2.) : h = 0 when it hits the ground, therefore: -16t^2 + 48t = 0 : Factor out -16t -16t(t + 3) = 0 : Two solutions t = 0, when it begins it's upward journey and t = 3 sec, when it returns to earth
 Linear-systems/206061: solve the following system of equations x +3y =9 (1) x=5-3y (2) 1 solutions Answer 155660 by ankor@dixie-net.com(16526)   on 2009-08-10 09:41:53 (Show Source): You can put this solution on YOUR website!x + 3y = 9 (1) x = 5 - 3y (2) ; Add 3y to both sides of the 2nd equation and you have: x + 3y = 9 x + 3y = 5 : Obviously, there is no solution to this system
 Linear-systems/206062: if trains a and b are travelin gthe same direction on parallel tracks. train a is traveling at 100 mph and train b is traveling 120 mph. train a passes a station at 9:20 am if train b passes the same station at 9:32 amd at what time will train b catch up to train A1 solutions Answer 155656 by ankor@dixie-net.com(16526)   on 2009-08-10 09:15:42 (Show Source): You can put this solution on YOUR website!if trains a and b are traveling the same direction on parallel tracks. train a is traveling at 100 mph and train b is traveling 120 mph. train a passes a station at 9:20 am if train b passes the same station at 9:32 and at what time will train b catch up to train A ; from the given information, we know that train B is 12 min (.2 hr) behind train A, when train A passes the station : The distance between the trains at this time: .2 * 120 = 24 mi : Let t = time required for train B to catch train a : write a distance equation: Dist = speed * time : Train b travel dist = Train a travel dist + 24 mi 120t = 100t + 24 120t - 100t = 24 120t = t = 1.2 hr or 1 hr 12 min : 9:20 + 1:12 = 10:32 pm, B catches A : : Check solution by finding the distances (train b travels 24 mi more than train b) 120 * 1.2 = 144 mi 100 * 1.2 = 120 mi ------------------- difference = 24 mi
 Quadratic_Equations/206041: 7x2-x+3k=0 Using quadradic equation, solve for k.1 solutions Answer 155627 by ankor@dixie-net.com(16526)   on 2009-08-09 21:55:37 (Show Source): You can put this solution on YOUR website!7x^2 - x + 3k = 0 : Find the factors that satisfy the coefficients of x^2 and x (7x + 6)(x - 1) = 0 Foil 7x^2 - 7x + 6x - 6 = 0 therefore 3k = -6 k = -6/3 k = -2
 Numbers_Word_Problems/206016: Betty found a number of nickels,dimes and quarters in her room. She found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was \$11.40. How many coins of each type did Betty find?1 solutions Answer 155619 by ankor@dixie-net.com(16526)   on 2009-08-09 20:51:48 (Show Source): You can put this solution on YOUR website!Betty found a number of nickels,dimes and quarters in her room. She found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was \$11.40. How many coins of each type did Betty find? : let n, d, q = no. of nickels, dimes and quarters respectively : Write an equation for the statements: "6 more dimes than nickels" d = n + 6 or n = (d-6) : " three times as many quarters as dimes." q = 3d ; "The total value of the coins was \$11.40." .05n + .10d + .25q = 11.40 : Substitute for n and q .05(d-6) + .10d + .25(3d) = 11.40 : .05d - .30 + .10d + .75d = 11.40 : .90d = 11.40 + .30 : .9d = 11.70 d = d = 13 dimes : How many coins of each type did Betty find? : Use the above equations : n = 13 - 6 n = 7 nickels ; q = 3(13) q = 39 quarters : : Check solution .05(7) + .10(13) + .25(39) = .35 + 1.30 + 9.75 = 11.40; confirms our solutions
 Quadratic_Equations/206022: Hi, Im having problems trying to solve this problem. Can you help. Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 57 points. they won 12 more games than they tied. How many wins did the team have? How many ties did the team have?1 solutions Answer 155605 by ankor@dixie-net.com(16526)   on 2009-08-09 18:52:06 (Show Source): You can put this solution on YOUR website!Hockey teams receive 2 points when they win and 1 point when they tie. One season, a team won a championship with 57 points. they won 12 more games than they tied. How many wins did the team have? How many ties did the team have? : let t = no. of ties then (t+12) = no. of wins : 2(t+12) + 1t = 57 2t + 24 + t = 57 2t + t = 57 - 24 3t = 33 t = t = 11 ties ; ; Check solution (11+12=23 wins) 23(2) + 11 = 57
 Polynomials-and-rational-expressions/206029: Please help me quickly. I don't have a lot of time left. I have been messing around with this problem for days and I can't get it. It's 3/4 = 1 - 3x-2/x+1 3 over 4 = 1 - 3x-2 over x+1 Thanks. 1 solutions Answer 155603 by ankor@dixie-net.com(16526)   on 2009-08-09 18:43:53 (Show Source): You can put this solution on YOUR website! = 1 - Multiply by 4(x+1) 4(x+1)* = 4(x+1)*1 - 4(x+1)* cancel the denominators, results: 3(x+1) = 4(x+1) - 4(3x-2) : multiply what's inside the brackets 3x + 3 = 4x + 4 - 12x + 8 : Arrange the x's on the left 3x - 4x + 12x = 4 + 8 - 3 : 11x = 9 x =
 Travel_Word_Problems/205995: 1- In a river that flows at 3 mph, a boat takes 1 hour longer to sail 36 miles upstream than to return. Find the speed of the boat in still water. 1 solutions Answer 155601 by ankor@dixie-net.com(16526)   on 2009-08-09 18:34:07 (Show Source): You can put this solution on YOUR website! In a river that flows at 3 mph, a boat takes 1 hour longer to sail 36 miles upstream than to return. Find the speed of the boat in still water. : Let s = speed of boat in still water then (s+3) = speed downstream and (s-3) = speed upstream : Write a time equation : time downstream = time upstream - 1 hr = - 1 : Multiply equation by (s+3)(s-3), results 36(s-3) = 36(s+3) - (s+3)(s-3)(1) : 36s - 108 = 36s + 108 - (s^2 - 9) : 36s - 108 = 36s + 108 - s^2 + 9 : Combine like terms on the left: s^2 + 36s - 36s - 108 - 108 - 9 = 0 : s^2 - 225 = 0 : s^2 = 225 s = s = 15 mph, speed in still water : : Check solution by finding the times 36/(15-3) = 3 hrs 36/(15+3) = 2 hrs ------------------ differs by: 1 hr
 Miscellaneous_Word_Problems/205864: paul's calculator can make only two operations : add 12 to the number displayed ,or subtract 7 from it. today, it shows the number 1998. what is the minimal number of steps needed to display the number 2000 ? A) 4 b) 12 c) 16 d) 21 e) 241 solutions Answer 155588 by ankor@dixie-net.com(16526)   on 2009-08-09 16:16:54 (Show Source): You can put this solution on YOUR website!paul's calculator can make only two operations : add 12 to the number displayed ,or subtract 7 from it. today, it shows the number 1998. what is the minimal number of steps needed to display the number 2000? : The resulting increase from repeating the two operations = +2 ; Let x = no. of +12 steps Let y = no. of -7 steps : 12x - 7y = 2 -7y = -12x + 2 7y = 12x - 2; multiplied by -1 y = x - ; Substitute values for x until you get an integer value for y x = 6 ea +12 steps y = (6)- y = - y = y = 10 ea -7 steps : Total 16 steps
 Travel_Word_Problems/205963: 1. Ramesh walks at 5/6th of his usual speed and reaches school 4 minutes late. Find the usual time taken by him to reach school. 2. Rakesh runs at 5/4 of his usual speed and reaches the playground 5 minutes earlier. What is his usual time/ 3.Two trains 110m and 100m long are running on parallel tracks, in the same direction with a speed of 46 km/hr and 39 km/hr respectively. How long will it take them to be clear of each other? 4. A cyclist A started his journey on cycle at 7.30 a.m. at speed 8km/hr. B another cyclist started from the same point half an hour later but with speed 10 km/hr. At what time did B overtake A?1 solutions Answer 155580 by ankor@dixie-net.com(16526)   on 2009-08-09 15:03:33 (Show Source): You can put this solution on YOUR website!1. Ramesh walks at 5/6th of his usual speed and reaches school 4 minutes late. Find the usual time taken by him to reach school. : Let s = usual walking speed then s = slower speed : Let t = usual time to walk to school then (t+4) = time required when walking slower : write a distance equation ts = (t+4)(s) ; multiply both sides by 6 6ts = 5s(t+4) 6ts = 5ts + 20s 6ts - 5ts = 20s ts = 20s Divide for sides by s, results : t = 20 min; normal time to walk to school ; : 2. Rakesh runs at 5/4 of his usual speed and reaches the playground 5 minutes earlier. What is his usual time/ : Let s = usual running speed then s = faster running speed : Let t = usual time to run to school then (t-5) = time required when running faster : write a distance equation ts = (t-5)(s) ; Multiply both side by 4 4ts = 5s(t-5) 4ts = 5ts - 25s 4ts - 5ts = -25s -ts = -25s Divide for sides by -s, results : t = 25 min; normal time running to school : : 3.Two trains 110m and 100m long are running on parallel tracks, in the same direction with a speed of 46 km/hr and 39 km/hr respectively. How long will it take them to be clear of each other? : The relative speed between the two trains: 46 - 39 = 7 km/hr : How long to travel 110+100 = 210m at 7 km/hr? : 210 m = .21 km: * 60 ~ 1.8 minutes : : 4. A cyclist A started his journey on cycle at 7.30 a.m. at speed 8km/hr. B another cyclist started from the same point half an hour later but with speed 10 km/hr. At what time did B overtake A? : Let t = B's travel time then (t+.5) = A's travel time : When B overtakes A, they will have traveled the same distance Write a distance equation : 10t = 8(t+.5) 10t = 8t + 4 10t - 8t = 4 2t = 4 t = t = 2 hrs is B's travel time ; He left at 8:00, therefore he overtakes A at 10:00 : : Check solution by ensuring their distances are equal 2*10 = 20 km 2.5* 8 = 20 km
 Miscellaneous_Word_Problems/205967: Alphonse starts at point A and runs at a constant rate towards point C. At the same time, Brigitte starts at point B and runs towards point C also at a constant rate. They arrive at C at exactly thesame moment. If they continue running in the same directions, Alphonse arrives at B exactly 10 seconds before Brigitte arrives at A. How fast was Brigitte running? A|----60m------|C---40m----|B1 solutions Answer 155570 by ankor@dixie-net.com(16526)   on 2009-08-09 13:27:37 (Show Source): You can put this solution on YOUR website!Alphonse starts at point A and runs at a constant rate towards point C. At the same time, Brigitte starts at point B and runs towards point C also at a constant rate. They arrive at C at exactly the same moment. If they continue running in the same directions, Alphonse arrives at B exactly 10 seconds before Brigitte arrives at A. How fast was Brigitte running? A|----60m------|C---40m----|B : Let a = Al's speed (in meters/sec) Let b = Brig's speed : They arrive at C at the same time equation, = cross multiply 40a = 60b a = a = 1.5b : Time for each running 100 meters equation B's time = A's time + 10 sec = + 10 : Replace a with 1.5b = + 10 : Multiply equation by 3 to get rid of the denominators, results 3(100) = 2(100) + 1.5b(10) : 300 = 200 + 15b : 300 - 200 = 15b : 100 = 15b b = b = 6 meters/sec is Brig's speed (that's 24 km/hr) : : Check solution Find A's speed: 1.5*6.667 ~ 10 meters/sec Find the times 60/10 = 6 sec 40/6.667 ~ 6 sec
 Rate-of-work-word-problems/205942: Pls. Help me I would like to know the proper solving of this question. Mariko can finish the typing job in 5 hrs. If Monique helps her, they can finish the same job in three hrs. How long would it take Monique to finish the typing job alone?1 solutions Answer 155563 by ankor@dixie-net.com(16526)   on 2009-08-09 12:35:41 (Show Source): You can put this solution on YOUR website!Mariko can finish the typing job in 5 hrs. If Monique helps her, they can finish the same job in three hrs. How long would it take Monique to finish the typing job alone? : Let x = amt of time required for Monique to do the job alone : Let the completed job = 1 ; Each will do a faction of the job, the two fraction add up to 1: + = 1 : Multiply equation by 5x to get rid of the denominator, results: 3x + 3(5) = 5x : 15 = 5x - 3x : 15 = 2x x = x = 7.5 hrs working alone : : Is this true: + = .6 + .4 = 1
 Percentage-and-ratio-word-problems/205939: Confusing. Help Pls. How much water must be added to 30 liters of a 75% salt solution to reduce it to 15%?1 solutions Answer 155559 by ankor@dixie-net.com(16526)   on 2009-08-09 12:22:24 (Show Source): You can put this solution on YOUR website!How much water must be added to 30 liters of a 75% salt solution to reduce it to 15%? : Let x = amt of water required to this : the amt salt remains the same, only the % salt changes A simple equation : .75(30) = .15(x + 30) : 22.5 = .15x + 4.5 : 22.5 - 4.5 = .15x : 18 = .15x x = x = 120 liters of water required : : Check solution original equation (equal amt of salt) .75(30) = .15(120 + 30) 22.5 = .15(150) 22.5 = 22.5 ; : Did this unconfuse you somewhat
 test/205971: A cyclist travels 80km from Paris to Louvre at an average speed of x km/h. Find the time taken in term of x. On his return journey from Louvre to Paris, he decreases his average speed by 3km/h. Find the time taken on the return journey in terms of x. If the difference between the times is one hour 20 minutes, find the value of x.1 solutions Answer 155550 by ankor@dixie-net.com(16526)   on 2009-08-09 11:30:37 (Show Source): You can put this solution on YOUR website!A cyclist travels 80km from Paris to Louvre at an average speed of x km/h. Find the time taken in term of x. f(x) = ; On his return journey from Louvre to Paris, he decreases his average speed by 3km/h. Find the time taken on the return journey in terms of x. f(x) = If the difference between the times is one hour 20 minutes, find the value of x. : Write a time equation: 20 min = hr : slow speed time - fast speed time = 20 min - = multiply equation by 3x(x-3), results 3x(80) - 3(x-3)*80 = x(x-3) : 240x - 240x + 720 = x^2 - 3x Arrange as a quadratic equation x^2 - 3x - 720 = 0 We have to use the quadratic formula here: in this problem a=1; b=-3; c=-720 : : : We want the positive solution here: x = x = x = 28.33 km/hr : ; Check solution, find the times 80/25.33 = 3.16 hrs 80/28.33 = 2.82 --------------- differs = .34 hr ~ 20 min
 Numbers_Word_Problems/205861: The numerator of a fraction is one more than the denominator. If the numerator and the denominator are both increased by 2, the new fraction will be one fourth less than the original fraction. What is the original fraction? Here's what I tried... n+1/n original fraction n+1+2/n+2 = n+1/n - 1/4 (n+1/n) Don't know if I have it set up correctly. Need help. THanks!1 solutions Answer 155500 by ankor@dixie-net.com(16526)   on 2009-08-08 21:25:56 (Show Source): You can put this solution on YOUR website!The numerator of a fraction is one more than the denominator. If the numerator and the denominator are both increased by 2, the new fraction will be one fourth less than the original fraction. What is the original fraction? : Looks like you are on the right track, here's how I would do it : Let x = the denominator "The numerator of a fraction is one more than the denominator." therefore: (x+1) = the numerator ; " If the numerator and the denominator are both increased by 2, the new fraction will be one fourth less than the original fraction." = - : = - Multiply equation by 4x(x+2) 4x(x+2)* = 4x(x+2)* - 4x(x+2)* Cancel the denominators: 4x(x+3) = 4(x+2)(x+1) - x(x+2) : 4x^2 + 12x = 4(x^2 + 3x + 2) - x^2 - 2x : 4x^2 + 12x = 4x^2 + 12x + 8 - x^2 - 2x Arrange as a quadratic equation on the left 4x^2 - 4x^2 + x^2 + 12x - 12x + 2x - 8 = 0 : x^2 + 2x - 8 = 0 Factors to: (x+4)(x-2) = 0 Positive solution x = 2 is the denominator then 2 + 1 = 3 is the numerator : What is the original fraction? : : Check solution in the statement: if the numerator and the denominator are both increased by 2, the new fraction will be one fourth less than the original fraction." = - = -
 Age_Word_Problems/205841: Mary's age and Bob's age are in the ration 3:2. Eight years later, the ratio of their ages will be 4:3. Find their present ages.1 solutions Answer 155493 by ankor@dixie-net.com(16526)   on 2009-08-08 20:56:29 (Show Source): You can put this solution on YOUR website!m = Mary's age; b = Bob's age : Mary's age and Bob's age are in the ration 3:2. = cross multiply 2m = 3b m = b or m = 1.5b : Eight years later, the ratio of their ages will be 4:3. = Cross multiply 3(m+8) = 4(b+8) 3m + 24 = 4b + 32 3m = 4b + 32 - 24 3m = 4b + 8 : Find their present ages. Replace m with 1.5b in the above equation 3(1.5b) = 4b + 8 4.5b = 4b + 8 4.5b - 4b = 8 .5b = 8 b = b = 16 yr is Bob's present age then m = 1.5(16) m = 24 yrs is Mary's present age ; : Check solution in the 8 yr equation =
 Linear-equations/205821: Find an equation of the line having the given slope and containing the given point. m=6,(7,1) the equation of the line in slope-intercept is y=1 solutions Answer 155425 by ankor@dixie-net.com(16526)   on 2009-08-07 19:26:52 (Show Source): You can put this solution on YOUR website!Find an equation of the line having the given slope and containing the given point. m=6,(7,1) : Start with the point/slope form: y - y1 = m(x - x1) y - 1 = 6(x - 7) y - 1 = 6x - 42 y = 6x - 42 + 1 : the equation of the line in slope-intercept is y = 6x - 41
 Travel_Word_Problems/205685: A car travels from one town to another town at a speed of 18mph. If it had gone 18mph faster, it could've made the trip in a half hour less time. How far a part are the towns?1 solutions Answer 155421 by ankor@dixie-net.com(16526)   on 2009-08-07 17:09:29 (Show Source): You can put this solution on YOUR website!A car travels from one town to another town at a speed of 18mph. If it had gone 18mph faster, it could've made the trip in a half hour less time. How far a part are the towns? : let d = dist between towns : Write a time equation: time = Actual speed time = 18 mph faster time + half hr = + multiply equation by 36, results 2d = d + 18 2d - d = 18 d = 18 min between towns ; ; Check solution find the times 18/18 = 1 hr 18/36 = .5 hr ------------- diff = .5 hr
 Travel_Word_Problems/205787: In Slippery Creek, Janna can row 50 km downstream in 5 hours or she can row 25 km upstream in the same amount of time. Find the rate she rows in still water.1 solutions Answer 155393 by ankor@dixie-net.com(16526)   on 2009-08-07 13:17:46 (Show Source): You can put this solution on YOUR website! Janna can row 50 km downstream in 5 hours or she can row 25 km upstream in the same amount of time. Find the rate she rows in still water. : let s = speed in still water let c = speed of the current ; write two distance equation Dist = time * speed : 5(s + c) = 50 5(s - c) = 25 : Simplify, divide both equations by 5 and you have: s + c = 10 s - c = 5 -------------addition eliminates c, find s 2s = 15 s = s = 7.5 km/hr in still water : : Is this true? Find the speed of the current s + c = 10 7.5 + c = 10 c = 10 - 7.5 c = 2.5 km/hr speed of the current : Check in the original equation 5(s + c) = 50 5(7.5 + 2.5) = 50 or 5(7.5 - 2.5) = 25
 Rational-functions/205754: Can you please help me with this problem 3/4=1-3x-2/x+11 solutions Answer 155374 by ankor@dixie-net.com(16526)   on 2009-08-07 09:36:24 (Show Source): You can put this solution on YOUR website!Assume the problem is: = 1 - : multiply the equation by 4(x+1) 4(x+1)* = 4(x+1)*1 - 4(x+1)* : cancel out the denominators and you have: 3(x+1) = 4(x+1) - 4(3x-2) : 3x + 3 = 4x + 4 - 12x + 8 : combine like terms 3x + 3 = -8x + 12 : 3x + 8x = 12 - 3 : 11x = 9 x = ; : Check the solution in the original equation, you can use the decimal .818 equiv to get a close check on it = 1 -
 Miscellaneous_Word_Problems/205467: Yogurt blends regular yogurt that is 3% fat with its no fat yogurt to obtain lowfat yogurt that is 1%. How many pounds of regular yogurt and how many pounds of no fat yogurt should be mixed to obtain 60 pounds of low fat yogurt?1 solutions Answer 155347 by ankor@dixie-net.com(16526)   on 2009-08-06 21:47:18 (Show Source): You can put this solution on YOUR website!Yogurt blends regular yogurt that is 3% fat with its no fat yogurt to obtain lowfat yogurt that is 1%. How many pounds of regular yogurt and how many pounds of no fat yogurt should be mixed to obtain 60 pounds of low fat yogurt? ; Let x = amt of 3% stuff : write am amt of fat equation, (amt of fat remains unchanged, the per cent changes) .03x = .01(60) : .03x = .6 : x = x = 20 lb of 3% stuff required then 60 - 20 = 40 lb of no fat (0%)
 Pythagorean-theorem/205492: The length of the Rhombus is 52cm. One of its diagonal is 48 cm. Find the length of the other diagonal and the area of the Rhombus.1 solutions Answer 155340 by ankor@dixie-net.com(16526)   on 2009-08-06 20:24:25 (Show Source): You can put this solution on YOUR website!The length of the Rhombus is 52cm. One of its diagonal is 48 cm. Find the length of the other diagonal and the area of the Rhombus. : you can see that the two diagonals form 4 identical right triangles The hypotenuse = 52 cm (one side) One leg = half the short diagonal which is 48cm = 24 cm The other leg = half the longer diagonal (x) : Find the other leg (x) x = x = 46.13 : 2 * 46.13 = 92.26 cm is the longer diagonal : The area will be the total area of the 4 right triangles : 2 * (46.13 * 24) = 2214.24 sq/cm; (area of the 4 triangles)
 Geometry_Word_Problems/205648: Mr. McGreggor is redesigning his garden. If the new width is half of the old wideth and the new length is 4 feet less than twice the old wide, the garden will be 24 square feet. Find the old width. Thank you, Connie1 solutions Answer 155308 by ankor@dixie-net.com(16526)   on 2009-08-06 15:33:28 (Show Source): You can put this solution on YOUR website! If the new width is half of the old width and the new length is 4 feet less than twice the old width, the garden will be 24 square feet. Find the old width. : Let x = the old width then .5x = the new width ; "new length is 4 feet less than twice the old width," (2x - 4) = new length : Area = length * width .5x(2x-4) = 24 : x^2 - 2x = 24 : x^2 - 2x - 24 = 0 ; Factors to (x-6)(x+4) = 0 : the positive solution is what we want here ; x = 6 ft; is the old width ; : Check solution: New width = .5(6) = 3 ft New length = 2(6) - 4 = 8 ft Area: 3 * 8 = 24 sq/ft "
 Geometric_formulas/205531: Two similar cones have radii of 4 and 3, respectively. What is the ratio of their volumes?1 solutions Answer 155294 by ankor@dixie-net.com(16526)   on 2009-08-06 14:27:11 (Show Source): You can put this solution on YOUR website!Two similar cones have radii of 4 and 3, respectively. What is the ratio of their volumes? : Write a fraction; large cone vol / small cone vol : Cancel: (1/3), pi, and h =
 Travel_Word_Problems/205665: a rectangular box with a square base is shown below. if the volume of the box is 256 cubic feet and the height of the box is one half the length of the side of the base, find the height of the box.1 solutions Answer 155292 by ankor@dixie-net.com(16526)   on 2009-08-06 14:18:54 (Show Source): You can put this solution on YOUR website!a rectangular box with a square base is shown below. if the volume of the box is 256 cubic feet and the height of the box is one half the length of the side of the base, find the height of the box. : Let x = the side of the square base then .5x = the height of the box : x * x * .5x = 256 : .5x^3 = 256 Mult equation by 2 x^3 = 512 If you don't know the cube root of 512, use a calc, 512^(1/3) x = 8 the height = 4 ft : : Check solution: 8 * 8* * 4 = 256
 test/205644: plz help me find this answer. A car travels a 750 km journey at an average speed of x km/h. If it had increased its speed by 18 km/h, the journey would have been 125 minutes shorter. Form an equation in x and show that it reduces to x²+ 18x= 6480. Solve this equation to find the value of x. Hence find the time taken when the car travels at x km/h. 1 solutions Answer 155279 by ankor@dixie-net.com(16526)   on 2009-08-06 13:04:34 (Show Source): You can put this solution on YOUR website!A car travels a 750 km journey at an average speed of x km/h. If it had increased its speed by 18 km/h, the journey would have been 125 minutes shorter. Form an equation in x and show that it reduces to x²+ 18x= 6480. Solve this equation to find the value of x. Hence find the time taken when the car travels at x km/h. : x = actual speed then (x+18) = faster speed : Write a time equation; time = : Actual time = faster time + 125 min = + multiply equation by 60x(x+18) 60x(x+18)* = 60x(x+18)* + 60x(x+18)* Cancel the denominator, results 60(x+18)*750 = 60x*750 + x(x+18)*125 : 45000(x+18) = 45000x + 125x(x+18) : 45000x + 810000 = 45000x + 125x^2 + 2250x : Arrange as a quadratic equation on the right 0 = 125x^2 + 2250x + 45000 - 45000 - 810000 0 = 125x^2 + 2250x - 810000 : Simplify, divide by 125 x^2 + 18x - 6480 = 0; the given equation : Solve for x by factoring the equation (or you can use the quadratic formula) (x-72)(x+90) = 0 Positive solution is what we want here: x = 72 km/hr ; : Is this true? find the time of each using decimals 750/72 = 10.4 750/90 = 8.3 (18km/hr faster) -------------- differ = 2.1 hrs which is 126 min ~ 125 min
 Travel_Word_Problems/205607: This question is from textbook Algebra structure and method Cindy and Dave left the dock to canoe downstream. Fifteen minutes later Tammy left by otorboat with the supplies. Since the motorboat traveled twice as fast as the anoe, it caught up with the canoe 3km from the dock. What was the speed of the motorboat?1 solutions Answer 155266 by ankor@dixie-net.com(16526)   on 2009-08-06 11:15:02 (Show Source): You can put this solution on YOUR website!Cindy and Dave left the dock to canoe downstream. Fifteen minutes later Tammy left by motorboat with the supplies. Since the motorboat traveled twice as fast as the canoe, it caught up with the canoe 3km from the dock. What was the speed of the motorboat? ; Speed will be in km/hr; change 15 min to .25 hrs : Let s = the motor boat speed then .5s = speed of the canoe) : Write time equation: (time = : Motor time + 15 min = Canoe time + .25 = Multiply equation by s, results 3 + .25s = 2(3) ; 3 + .25s = 6 : .25s = 6 - 3 s = s = 12 km/h motorboat speed : : Check solution, find the travel times 3/6 = .5 hrs 3/12= .25 hrs --------------- diff = .25 hrs (15 min)
 Travel_Word_Problems/205628: At the moment when its altitude is 300 m, a plane is flying with a horizontal speed of 200km per hour and an unknown vertical speed. What is the minimum average vertical speed,in km/hr, required to avoid a 500 m tall mountain situated at a horizontal distance of 1km away from the plane? (A)30 (B)40 (C)100 (D) 200 (E) None of these 1 solutions Answer 155264 by ankor@dixie-net.com(16526)   on 2009-08-06 10:56:30 (Show Source): You can put this solution on YOUR website!At the moment when its altitude is 300 m, a plane is flying with a horizontal speed of 200km per hour and an unknown vertical speed. What is the minimum average vertical speed,in km/hr, required to avoid a 500 m tall mountain situated at a horizontal distance of 1km away from the plane? : Plane required to gain 500 - 300 = 200 meters : Determine how many seconds the plane is from the mountain at a horizontal speed of 200 km/hr. : * 3600 = 18 sec : Find the vertical speed required to go up 200 meters, in km/hr * 3600 * = 40 km/hr vertical speed (minimum)
 Finance/205475: Word Problem: A certain metal is 40% tin. How many kilograms of this metal must be mixed with 50kg of metal that is 60% tin to get a metal that is 50% tin? Please include the solution. Thank you very much1 solutions Answer 155155 by ankor@dixie-net.com(16526)   on 2009-08-05 14:50:54 (Show Source): You can put this solution on YOUR website!A certain metal is 40% tin. How many kilograms of this metal must be mixed with 50kg of metal that is 60% tin to get a metal that is 50% tin? : Let x = amt of 40% time required to do this : A typical mixture equation: .40x + .60(50) = .50(x+50) : .4x + 30 = .5x + 25 : 30 - 25 = .5x - .4x : 5 = .1x x = x = 50 kg of 40% tin ; : Check solution in original equation .40(50) + .60(50) = .50(50+50)
 Miscellaneous_Word_Problems/205482: The ratio of two sums of money is 4:3. If the larger sum of money is increased by 40\$, the ratio becomes 2:1. Find the sum of the money.1 solutions Answer 155154 by ankor@dixie-net.com(16526)   on 2009-08-05 14:41:46 (Show Source): You can put this solution on YOUR website!The ratio of two sums of money is 4:3. If the larger sum of money is increased by 40\$, the ratio becomes 2:1. Find the sum of the money. : Two sums of money:, x & y "The ratio of two sums of money is 4:3." = Cross multiply 3x = 4y x = y : " If the larger sum of money is increased by 40\$, the ratio becomes 2:1." = Cross multiply 2y = (x+40) : Find the sum of the money. Replace x with y in the above equation 2y = y + 40 multiply equation by 3 to get rid of the denominator 3(2y) = 3*y + 3(40) 6y = 4y + 120 6y - 4y = 120 2y = 120 y = \$60 is the smaller amt : find x x = (60) x = 4(20) x = \$80 is the larger amt