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 Travel_Word_Problems/466759: A relay race required runners to run from Point A to Point B and then back to point A. the distance from A to B = 22km. On the return trip (Point B to Point A) the runners average speed decreased by (1.2km/hr). If the relay took 10.5 hours to complete, what was the average speed from Point A to Point B. Thank You1 solutions Answer 320051 by ankor@dixie-net.com(15649)   on 2011-07-03 13:56:28 (Show Source): You can put this solution on YOUR website!A relay race required runners to run from Point A to Point B and then back to point A. the distance from A to B = 22km. On the return trip (Point B to Point A) the runners average speed decreased by (1.2km/hr). If the relay took 10.5 hours to complete, what was the average speed from Point A to Point B. : Let s = av speed from Point A to B : It says,"On the return trip (Point B to Point A) the runners average speed decreased by (1.2km/hr)." therefore: (s-1.2) = return trip speed (B to A) : Write a time equation; time = dist/speed + = 10.5 ; Multiply by s(s-1.2), results: 22(s-1.2) + 22s = 10.5s(s-1.2) : 22s - 26.4 + 22s = 10.5s^2 - 12.6s : 44s - 26.4 = 10.5s^2 - 12.6s : 0 = 10.5s^2 - 12.6s - 44s + 26.4 : A quadratic equation 10.5s^2 - 56.6s + 26.4 = 0 ; Multiply by 10 to get rid of the decimals 105s^2 - 566s + 264 = 0 : Use the quadratic formula to solve this a=105, b=-566, c=264, s=x : : Two solutions, but only this one will make sense s = s = 4.87 km/hr, av speed from A to B : : Check this by finding the times 22/4.87 = 4.5 hrs 22/3.67 = 6.0 hrs ----------------- tot time: 10.5 hrs, confirms our solution
 Age_Word_Problems/466556: Please help. The sum of the ages of Art, Ben, and Cal is 59. Art is 1 year older than Cal and Cal is 1 year younger than Ben. Which of these people were teenagers 7 years ago?1 solutions Answer 319949 by ankor@dixie-net.com(15649)   on 2011-07-02 21:28:33 (Show Source): You can put this solution on YOUR website!Write an equation for each statement: ; The sum of the ages of Art, Ben, and Cal is 59. a + b + c = 59 : Art is 1 year older than Cal a = (c+1) : and Cal is 1 year younger than Ben. c = b - 1 or b = (c+1) Looks like a & b are the same age : Replace a and b in the 1st equation (c+1) + (c+1) + c = 59 3c = 59 - 2 3c = 57 c = c = 19 yrs then a & b = 20 yrs Which of these people were teenagers 7 years ago? All of them
 Mixture_Word_Problems/466582: Hello, I have a question I need help with. Your time is appreciated. How many gallon of a 5% acid solution must be mixed with 30 gallons of 10% acid solution to obtain a mixture that is 8% acid? Thank you1 solutions Answer 319945 by ankor@dixie-net.com(15649)   on 2011-07-02 21:14:47 (Show Source): You can put this solution on YOUR website!How many gallon of a 5% acid solution must be mixed with 30 gallons of 10% acid solution to obtain a mixture that is 8% acid? : Let x = amt of 5% acid required to accomplish this : Write the decimal equiv of the percent acid equation : .05x + .10(30) = .08(x+30) .05x + 3 = .08x + 2.4 3 - 2.4 = .08x - .05x .6 = .03x x = x = 20 gal of 5% acid required : : Check this .05(20) + .10(30) = .08(20+30) 1 + 3 = .08(50) 4 = 4; confirms our solution
 Evaluation_Word_Problems/466432: i seriously need some help with this problem! in 1993, the life expectancy of males in a certain country was 66.8 years. in 2000, it was 70.4 years. let E represent the life expectancy in year t and let t represent the number of years since 1993. the linear function that fits the data is E(t) = ?t + ? use the function to predict the life expectancy of males in 2003. E(10) = ?1 solutions Answer 319925 by ankor@dixie-net.com(15649)   on 2011-07-02 19:42:42 (Show Source): You can put this solution on YOUR website!In 1993, the life expectancy of males in a certain country was 66.8 years. in 2000, it was 70.4 years. let E represent the life expectancy in year t and let t represent the number of years since 1993. : Find the slope In 1993; x1=0 and y1=66.8 In 2000; x2=7 and y2=70.4 : Find the slope (m) using the slope equation: m = m = = = : Use the point/slope formula to write the equation; y - y1 = m(x - x1) y - 66.8 = (x - 0) y = x + 66.8 : therefore: The Linear function E(t) that fits the data is. E(t)= t + 66.8 : Use the Function to predict the life expectancy of males in 2003. This means t=10; substitute 10 for t in the equation E(10)= (10) + 66.8 E(10)= 5.1 + 66.8 E(10)~ 72 yrs is the life expectancy in 2003
 Word_Problems_With_Coins/466563: Hello, I have a question I need help answering. Your time is appreciated. In Jose's coin jar there is a collection of nickels, dimes, and quarters which totals \$4.05. There are twice as many quarters as nickels and 8 more dimes than nickels. How many coins of each kind are there?1 solutions Answer 319914 by ankor@dixie-net.com(15649)   on 2011-07-02 18:46:31 (Show Source): You can put this solution on YOUR website!coin jar there is a collection of nickels, dimes, and quarters which totals \$4.05. There are twice as many quarters as nickels and 8 more dimes than nickels. How many coins of each kind are there? : Let n = no.of nickel Let d = no. of dimes let q = no. of quarters : Write an equation for each statement: : "coin jar there is a collection of nickels, dimes, and quarters which totals \$4.05." .05n + .10d + .25q = 4.05 : "There are twice as many quarters as nickels" q = 2n : "and 8 more dimes than nickels." d = (n+8) : In the 1st equation, replace q with 2n, replace d with (n+8) .05n + .10(n+8) + .25(2n) = 4.05 .05n + .10n + .8 + .50n = 4.05 .05n + .10n + .50n = 4.05 - 80 .65n = 3.25 n = n = 5 nickels : I'll let you find d and q, check solutions in the total\$ equation.
 Polynomials-and-rational-expressions/466394: Solve using the elimination method 1. -2x – 8y = 22 -6x – y = 20 2. x + 8y = 14 -3x + 4y = 0 3. 9x – 7y = -120.5 -36x + 28y = -482 Thank You So Much For Your Help! 1 solutions Answer 319906 by ankor@dixie-net.com(15649)   on 2011-07-02 18:10:25 (Show Source): You can put this solution on YOUR website!Solve using the elimination method 1. -2x – 8y = 22 -6x – y = 20 Multiply the 1st equation by -3: +6x + 24y = -66 -6x - y = 20 ------------------adding eliminates x find y 23y = -46 y = y = -2 Find x using the 1st equation -2x - 8(-2) = 22 -2x + 16 = 22 -2x = 22 - 16 -2x = 6 x = x = -3 Check solutions in the 2nd equation -6x - y = 20 -6(-3) - (-2) = +18 + 2 = 20 : : 2. x + 8y = 14 -3x + 4y = 0 multiply the 1st equation by 3, do it the same way we did the 1st one : : 3. 9x – 7y = -120.5 -36x + 28y = -482 multiply the 1st equation by 4 +36x - 28y = -482 -36x + 28y = -482 these lines are parallel. No solution
 Age_Word_Problems/466550: heather is twice as old as armida while kaye is 35 years youner than heather. if 1/2 the age ofarmida 5 years ago , and 1/3 of the age of heathr 10 years from now is twice the age of kaye, how old is kaye now? 1 solutions Answer 319895 by ankor@dixie-net.com(15649)   on 2011-07-02 16:24:40 (Show Source): You can put this solution on YOUR website!Heather is twice as old as Armida while Kaye is 35 years younger than Heather. If 1/2 the age of Armida 5 years ago, and 1/3 of the age of Heather 10 years from now, is twice the age of Kaye, how old is Kaye. : Let h = Heather's present age Let a = Armida's Let k = Kaye's : Write an equation for each statement: : "Heather is twice as old as Armida" h = 2a or a = .5h : "while Kaye is 35 years younger than Heather." k = h - 35 or h = (k+35) : we need to get a in terms of k also a = .5(k+35) a = (.5k+17.5) : "If 1/2 the age of Armida 5 years ago, and 1/3 of the age of Heather 10 years from now, is twice the age of Kaye," (a-5) + (h+10) = 2k : multiply by 6 to clear the denominators, results: 3(a-5) + 2(h+10) = 6(2k) 3a - 15 + 2h + 20 = 12k 3a + 2h + 5 = 12k replace h with 2a 3a + 2(2a) + 5 = 12k 3a + 4a + 5 = 12k 7a + 5 = 12k Replace a with (.5k+17.5)) 7(.5k+17.5) + 5 = 12k 3.5k + 122.5 + 5 = 12k 3.5k + 127.5 = 12k 127.5 = 12k - 3.5k 127.5 = 8.5k k = k = 15 yrs is Kaye's age : : A lot of chances to make a mistake here, check this: h = 15 + 35 = 50 a = .5(50) = 25 Use these values in the statement: "If 1/2 the age of Armida 5 years ago, and 1/3 of the age of Heather 10 years from now, is twice the age of Kaye," (25-5) + (50+10) = 2(15) (20) + (60) = 30 10 + 20 = 30; confirms are solution
 Linear_Equations_And_Systems_Word_Problems/466521: When Simon was born, his father was 36 years old. Five years ago, his father was twice as old as Simon will be in 7 years time. How old is Simon?1 solutions Answer 319890 by ankor@dixie-net.com(15649)   on 2011-07-02 15:15:53 (Show Source): You can put this solution on YOUR website!When Simon was born, his father was 36 years old. Five years ago, his father was twice as old as Simon will be in 7 years time. How old is Simon? : Let s = Simon's age Let f = father's age : Write an equation for each statement: : "When Simon was born, his father was 36 years old." f = s + 36 : "Five years ago, his father was twice as old as Simon will be in 7 years time." f - 5 = 2(s+7) f - 5 = 2s + 14 f = 2s + 14 + 5 f = 2s + 19 Replace f with (s+36) f + 36 = 2s + 19 36 - 19 = 2s - s 17 = s, Simon is 17 yrs old : : Check solution in the statement (father is: 17 + 36 = 53 yrs old) "Five years ago, his father was twice as old as Simon will be in 7 years time" 53 - 5 = 2(17 + 7) 48 = 2(24)
 Square-cubic-other-roots/466491: Simplify by taking roots of the numerator and the denominator. assume that all expressions under radicals represent positive numbers. (I'm lost on this one!) SQRT125x^11/y^31 solutions Answer 319888 by ankor@dixie-net.com(15649)   on 2011-07-02 15:03:30 (Show Source): You can put this solution on YOUR website! Factor inside the radical to reveal the squares extract those square roots
 Age_Word_Problems/466517: A woman had seven children. On multiplying their ages together, one can obtain the number 6591. Given that today is the birthday of all seven children, how many triplets are there and what are all the seven ages?1 solutions Answer 319834 by ankor@dixie-net.com(15649)   on 2011-07-02 08:10:17 (Show Source): You can put this solution on YOUR website!A woman had seven children. On multiplying their ages together, one can obtain the number 6591. Given that today is the birthday of all seven children, how many triplets are there and what are all the seven ages? : Prime factor: 3 * 13 * 13 * 13 = 6591 : How about two sets of triplets, ages 1, and ages 13, one child age 3? for ages, 1 * 1 * 1 * 3 * 13 * 13 * 13 = 6591
 Length-and-distance/466414: During the first part of a trip, a canoeist travels 59 miels at a certain speed. The canoeist travels 25 miles on the second part of the trio at a speed of 5 mph slower. The total time for the trip is 5 hrs. What was the speed of each part of the trip.1 solutions Answer 319786 by ankor@dixie-net.com(15649)   on 2011-07-01 22:07:36 (Show Source): You can put this solution on YOUR website!During the first part of a trip, a canoeist travels 59 miles at a certain speed. The canoeist travels 25 miles on the second part of the trio at a speed of 5 mph slower. The total time for the trip is 5 hrs. What was the speed of each part of the trip. : Let s = speed on the 1st part of the trip then (s-5) = speed on the 2nd part : Write a time equation; time = dist/speed : 1st part time + 2nd part time = 5 hrs + = 5 multiply by s(s-5), results; 59(s-5) + 25s = 5s(s-5) : 59s - 295 + 25s = 5s^2 - 25s : 84s - 295 = 5s^2 - 25s : Arrange as a quadratic equation on the right 0 = 5s^2 - 25s - 84s + 295 : 5s^2 - 109s + 295 = 0 : use the quadratic formula to find s, only one solution will make sense
 Rectangles/466398: I was doing an IQ game ("challenging" level) and was faced with a problem, which I solved by logical thinking and trial/error. However, before that I tried to figure out a way to solve the problem with algebra. I'm still not sure if it is possible or not. The problem/question: "Charlie removed a one-metre wide strip of grass from all the way around a square lawn, which was made info a flower bed. The remaining grass was four-fifths the area of the new flower bed. What were the dimensions of the lawn originally?" It seemed to me that we are missing a value (a length), but then I thought that it might be possible to figure it out by using equations, and canceling out values against each other. I tried different approaches, but I haven't done equations for a long time and got stuck. This was my approach: a = length or height of square lawn b = new flower bed c = remaining grass d = dimensions of original lawn (area) c = 4/5b d = b + c (a - 2)x2 = (4/5b) + (5/5b) Is it just not possible, or am I missing something? Any help with pointing out if and how this can be done would be greatly appreciated! Kind regards, Rob1 solutions Answer 319737 by ankor@dixie-net.com(15649)   on 2011-07-01 18:47:24 (Show Source): You can put this solution on YOUR website!Charlie removed a one-metre wide strip of grass from all the way around a square lawn, which was made into a flower bed. The remaining grass was four-fifths the area of the new flower bed. What were the dimensions of the lawn originally? : Let the original dimension of the square lawn = x by x Area of original lawn = x^2 : After removing the 1 meter strip all the way around, the dimensions would be: (x-2) by (x-2) Area of the remaining grass = (x-2)^2, FOIL this and you have: A = x^2 - 4x + 4; the remaining grass : then find removed strip area: A = x^2 - (x^2 - 4x + 4) A = x^2 - x^2 + 4x - 4 A = 4x - 4, the area of the flowerbed : x^2 - 4x + 4 = (4x - 4) :
 Quadratic_Equations/466249: Problem Solving: A sunflower plant was purchased with the following growth guarantee. After being planted, on the first day it would grow 100 mm. On the second day its height would increase by one half (50%), on the third day by one third, on the fourth day by one fourth, and so on. Assuming that the plant actually grows according to the guarantee, how many days would it take for it to reach its maximum height of 5000 mm?1 solutions Answer 319672 by ankor@dixie-net.com(15649)   on 2011-07-01 12:02:43 (Show Source): You can put this solution on YOUR website!A sunflower plant was purchased with the following growth guarantee. After being planted, on the first day it would grow 100 mm. On the second day its height would increase by one half (50%), on the third day by one third, on the fourth day by one fourth, and so on Assuming that the plant actually grows according to the guarantee, how many days would it take for it to reach its maximum height of 5000 mm? : Day 1: 100 Day 2: 100 + *100 = 150 Day 3: 150 + *150 = 200 Day 4: 200 + *200 = 250 Day 5: 250 + *250 = 300 Day 6: 300 + *300 = 350 Day 7: 350 + *350 = 400 From this we can see a pattern, that every day it will increase by 50: 50(d+1) = 5000 50d + 50 = 5000 50d = 5000 - 50 50d = 4950 d = d = 99 days to reach 5000 mm
 Numbers_Word_Problems/465912: If 1 more than a certain number is 3 less than a second number, the larger of these numbers minus he smaller is equal to1 solutions Answer 319645 by ankor@dixie-net.com(15649)   on 2011-07-01 08:47:44 (Show Source): You can put this solution on YOUR website!If 1 more than a certain number is 3 less than a second number, the larger of these numbers minus he smaller is equal to: : Let x = "a certain number" Let y = "a second number" : x + 1 = y - 3 x = y - 3 - 1 x = y - 4 we can rewrite this to y - x = 4 which answers the statement,"the larger of these numbers minus he smaller is equal to"
 Linear-systems/466169: Joe orders an 8 ounce martini that is 4.7% vermouth. sue orders an 8 ounce martini that is 100% gin. a martini is made with gin and vermouth. Joe and Sue give the drinks to Jane. Jane would like to mix a portion of each drink, so that she has an 8 ounce martini that is 99.8% gin. How much does Jane use of each drink?1 solutions Answer 319542 by ankor@dixie-net.com(15649)   on 2011-06-30 21:27:24 (Show Source): You can put this solution on YOUR website!Joe orders an 8 ounce martini that is 4.7% vermouth. sue orders an 8 ounce martini that is 100% gin. a martini is made with gin and vermouth. Joe and Sue give the drinks to Jane. Jane would like to mix a portion of each drink, so that she has an 8 ounce martini that is 99.8% gin. How much does Jane use of each drink? : Let x = amt of Sue's drink which is pure gin then (8-x) = amt of Joe's drink which is 4.7% vermouth Change Joes drink to per cent gin: 100 - 4.7 = 95.3% gin : Write a decimal equiv of per cent gin equation Sues + Joes = Jane's x + .953(8-x) = .998(8) x + 7.624 - .953x = 7.984 x - .953x = 7.984 - 7.624 .047x = .36 x = x = 7.66 oz of pure gin from Sue's drink then 8 - 7.66 = .34 oz of Joe's drink
 Surface-area/466166: hi, please help me with this word problem. The surface area of a cube is 864 square inches. Find the length of the lateral edge of the cube. thank youu1 solutions Answer 319540 by ankor@dixie-net.com(15649)   on 2011-06-30 21:00:33 (Show Source): You can put this solution on YOUR website!The surface area of a cube is 864 square inches. Find the length of the lateral edge of the cube : The surface area of a cube = 6x^2 : 6x^2 = 864 x^2 = x^2 = 144 x = x = 12 inches
 Linear_Equations_And_Systems_Word_Problems/466060: The height of an object thrown upward from the floor of a canyon 106 ft. deep, with an initial velocity of 120 ft/sec is given by the equation: h=-16t2 + 120t-106 How long will it take the object to rise to the height of the canyon wall? Round answer to the nearest hundreth.1 solutions Answer 319484 by ankor@dixie-net.com(15649)   on 2011-06-30 16:00:01 (Show Source): You can put this solution on YOUR website!The height of an object thrown upward from the floor of a canyon 106 ft. deep, with an initial velocity of 120 ft/sec is given by the equation: h=-16t2 + 120t-106 How long will it take the object to rise to the height of the canyon wall? Round answer to the nearest hundreth. : Height of the canyon wall = 0, depth of the canyon -106, so we have -16t^2 + 120t - 106 = 0 Use the quadratic formula: In this equation: t=x, a=-16, b-120, c=-106 : : Two solutions t = t = 1.023 sec, this is the solution we want, time at the top of the wall on the way up
 Miscellaneous_Word_Problems/466096: Please help me answer this question, thanks(: The price per person of renting a bus varies inversely with the number of people renting the bus. It costs \$20 per person if 56 people rent the bus. How much will it cost per person if 58 people rent the bus?1 solutions Answer 319447 by ankor@dixie-net.com(15649)   on 2011-06-30 14:21:22 (Show Source): You can put this solution on YOUR website!The price per person of renting a bus varies inversely with the number of people renting the bus. It costs \$20 per person if 56 people rent the bus. How much will it cost per person if 58 people rent the bus? : You can use an inverse proportion equation, x = cost when 58 people rent it = 58x = 20*56 x = x = \$19.31 : or Find the original total cost of the bus 20 * 56 = \$1120 : find the cost per person when 58 people rent it = \$19.31
 Travel_Word_Problems/465940: how can i calculate average speed when a plane is flying from one city to another and is 550 miles per hour and is 430 miles per hour on the return flight.1 solutions Answer 319431 by ankor@dixie-net.com(15649)   on 2011-06-30 13:29:30 (Show Source): You can put this solution on YOUR website!calculate average speed when a plane is flying from one city to another and is 550 miles per hour and is 430 miles per hour on the return flight. : Let a = the average speed for the round trip Let d = the one-way dist : Write a time equation: time = dist/speed : outbound time + return time = total time + = Actually we don't need d, just put it in here to illustrate what we are doing here Divide thru by d, and we have: + = Multiply by 23650a to clear the denominators, results 43a + 55a = 47300 98a = 47300 a = a = 482.653 mph is the average speed : : You can confirm this solution by choosing a value for d and finding the total of the actual times.
 Numbers_Word_Problems/465822: a five digit even number product of one's place and hundreds place is six and the sum is five tens place is greatest even number 1 solutions Answer 319418 by ankor@dixie-net.com(15649)   on 2011-06-30 12:33:51 (Show Source): You can put this solution on YOUR website!The problem as I understand it: : A five digit even number: The product of the one's place and hundreds place is six. The sum is five times the tens place. What is greatest even number? : Five digits, a, b, c, d, e : "The product of the one's place and hundreds place is six" e * c = 6 Since the number is even, e = 2, therefore c = 3 : "The sum is five times the tens place." e + c = 5d 2 + 3 = 5d 5 = 5d d = 1 : The greatest even number: 99312