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 Functions/167607: This is another form of problem that I am having trouble with. I would appreciate any help you can give me. d varies inversely as w and directly as the square of v. If d=40 when w=6 and v=2, find d when w=9 and v=4. d=kv2 40=k(4)2 40=k(16) 40/16=k 5/2=k1 solutions Answer 123544 by ankor@dixie-net.com(15657)   on 2008-11-14 19:01:20 (Show Source): You can put this solution on YOUR website!d varies inversely as w and directly as the square of v. This translates to: d = : If d=40 when w=6 and v=2, 40 = Find k = 40 : Multiply both sides by 6 4k = 6*40 4k = 240 k = k = 60 ; The equation: d = find d when w=9 and v=4. d = d = d = d = 106
 Mixture_Word_Problems/167609: 9. If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks? A. 2 minutes and 44 seconds B. 2 minutes and 58 seconds C. 3 minutes and 10 seconds D. 3 minutes and 26 seconds E. 4 minutes and 15 seconds 10. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it? A. 0.8 days B. 1.09 days C. 1.23 days D. 1.65 days E. 1.97 days I dont know how to do this type of question. Can you PLEASE explain?1 solutions Answer 123508 by ankor@dixie-net.com(15657)   on 2008-11-14 14:49:03 (Show Source): You can put this solution on YOUR website!9. If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks? : Here's an easy way to do this: Let t = time (in min) required when they work together to mix 20 drinks Let the completed job = 1; (the mixing of 20 drinks) : Each person does a fraction of the job and their fractions add up to 1 + + = 1 Multiply equation by 30 to get rid of he denominators, resulting in: 6t + 3t + 2t = 30 : 11t = 30 t = = 2 & 8/11 min, Change 8/11 min to seconds; 8/11 * 60 = 43.636 t = 2 min 44 sec : : 10. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it? : Same on this one. Let t = time (in days) working together Let the completed job = 1 ; + + = 1 : The common denominator will be 12, multiply the equation by 12 and see if you can do this one yourself. If you can't, let me know
 Complex_Numbers/167398: PLEASE HELP!!! MUST SHOW WORK. 1. simplify: 4xy^3/z^2 / (8x^2y/z^3)^2 2. Simplify d/d^2-9+5/2d+6 Thanks1 solutions Answer 123506 by ankor@dixie-net.com(15657)   on 2008-11-14 14:31:26 (Show Source): You can put this solution on YOUR website!1. simplify: : ------------- : Square the denominator fraction ------------- : Invert the dividing fraction and multiply, cancel like terms * = : 2. Simplify : + : Factor, then put over a common denominator: + = = =
 Travel_Word_Problems/167469: Help! At the Indianapolis 500, Carter and Daniels were participants. Daniels'motor blew after 240 miles, and Carter was out after 270 miles. If Carter's average rate was 20mph more than Daniels, and their total time was 3 hours, how fast was each averaging? Thank you for your help, whichever kind person answers my question! Lauren1 solutions Answer 123404 by ankor@dixie-net.com(15657)   on 2008-11-13 21:27:22 (Show Source): You can put this solution on YOUR website!At the Indianapolis 500, Carter and Daniels were participants. Daniel's motor blew after 240 miles, and Carter was out after 270 miles. If Carter's average rate was 20mph more than Daniels, and their total time was 3 hours, how fast was each averaging? ; Let s = D's speed then (s+20) = C's speed : Write a time equation: Time = dist/speed : D's time + C's time = 5 hrs + = 3 : Multiply equation by s(s+20) s(s+20)* + s(s+20)* = s(s+20)*3 ; Cancel out the denominators and you have: 240(s+20) + 270s = 3s(s+20) : 240s + 4800 + 270s = 3s^2 + 60s : 510s + 4800 = 3s^2 + 60s ; 0 = 3s^2 + 60s - 510s - 4800 : A quadratic equation 3s^2 - 450s - 4800 = 0 : Simplify divide by 3 s^2 - 150s - 1600 = 0 : Factors to: (s - 160)(x + 10) = 0 : Positive solution is what we want here: s = +160 mph is D's speed then 160 + 20 = 180 mph is C's speed. : : Check solution in original time equation + = 1.5 + 1.5 = 3 hrs; confirms our solution : by a kind person!
 Travel_Word_Problems/167461: Dick's motorboat can make an average 8 miles an hour. One day he sets out for a trip, only to have the motor break down. Dick rows back at 2 miles an hour. When he reaches his dock, he finds that he has been gone for 5 hours. How far has he rowed?1 solutions Answer 123398 by ankor@dixie-net.com(15657)   on 2008-11-13 21:03:54 (Show Source): You can put this solution on YOUR website!Dick's motorboat can make an average 8 miles an hour. One day he sets out for a trip, only to have the motor break down. Dick rows back at 2 miles an hour. When he reaches his dock, he finds that he has been gone for 5 hours. How far has he rowed? : Let d = distance rowed (same as by motor) ; Write a time equation. Time = : Motor time + rowing time = 5 hrs + = 5 : Multiply equation by 8 to get rid of the denominators, results: d + 4d = 8(5) : 5d = 40 d = d = 8 miles rowed : : Check solution in our equation + = 5
 Percentage-and-ratio-word-problems/167511: Hello here is a word problem: Due to melting, an ice sculpture loses one-half its weight every hour. After 8 hours, it weights 5/16 of a pound. How much did it weigh in the beginning? I know the answer is 80lb but don't understand how to set the problem up. Thank you for helping.1 solutions Answer 123391 by ankor@dixie-net.com(15657)   on 2008-11-13 20:53:32 (Show Source): You can put this solution on YOUR website!Due to melting, an ice sculpture loses one-half its weight every hour. After 8 hours, it weights 5/16 of a pound. How much did it weigh in the beginning? ; Use the decay formula: A = Ao(2^(-t/h)) where Ao is initial amt (what we are solving for) A = resulting amt (5/16) t = time in hrs (8) h = time required for substance to lose half it's weight (1hr) : Ao(2^(-8/1)) = .3125; (decimal value for 5/16) ; Using a calc find 2^-8 Ao * .0039 = .3125 Ao = Ao = 80.1 ~ 80 lbs
 Age_Word_Problems/167468: Ben's age is four years less than three times that of his younger sister Amy. Half of Ben's age increased by Amy's age is 2 years more than twice Amy's age. Find their ages.1 solutions Answer 123378 by ankor@dixie-net.com(15657)   on 2008-11-13 19:17:47 (Show Source): You can put this solution on YOUR website!Let b = Ben's age now Let a = Amy's age now ; Write an equation for each statement: : "Ben's age is four years less than three times that of his younger sister Amy." b = 3a - 4 : " Half of Ben's age increased by Amy's age is 2 years more than twice Amy's age." b + a = 2a + 2 subtract a from both sides b = 2a - a + 2 b = a + 2 Multiply both sides by 2 to get rid of the fraction b = 2(a+2) b = 2a + 4 : Find their ages. ; Substitute (3a-4) for b in the above equation 3a - 4 = 2a + 4 : 3a - 2a = 4 + 4 : a = 8 yrs is Amy's age : Find b b = 2a +4 b = 2(8) + 4 b = 20 yrs is Ben's age : : Check solution in the statement: " Half of Ben's age increased by Amy's age is 2 years more than twice Amy's age." 20 + 8 = 2(8) + 2 10 + 8 = 16 + 2
 Rectangles/167385: A farmer wants to build two rectangular pens of the same size next to a river so that they are separated by one fence. If she has 240 meters of fencing and does not fence the side next to the river, what are the dimensions of the largest area she can enclose? What is the largest area?1 solutions Answer 123358 by ankor@dixie-net.com(15657)   on 2008-11-13 16:52:52 (Show Source): You can put this solution on YOUR website!A farmer wants to build two rectangular pens of the same size next to a river so that they are separated by one fence. If he has 240 meters of fencing and does not fence the side next to the river, what are the dimensions of the largest area she can enclose? : We will have 3 sides = to the width (W), and 1 side equal to the length: Fencing equation: 3W + L = 240 : L = 240-3W : Area = L*W Substitute (240-3W) for L A = (240-3W)* W A = -3W^2 + 240W : Max area occurs at the axis of symmetry of this equation W = W = W = 40 ft : Find L L = 240-3(40) L = 240 - 120 L = 120 ft : What is the largest area? ; 120 * 40 = 4800 sq/ft : : you can also confirm this in the equation, substitute 40 for W
 Quadratic_Equations/167426: This question is from textbook The annual yield per lemon tree is fairly constant at 320 pounds when the number of trees per acre is 50 or fewer. For each additional tree over 50, the annual yield per tree for all trees on the acre decreases by 4 pounds due to overcrowding. Find the number of trees that should be planted on an acre to produce the maximum yield. How many pounds is the maximum yield? I understand the concept of max and min. What I can't get is the quadratic function. 1 solutions Answer 123345 by ankor@dixie-net.com(15657)   on 2008-11-13 15:24:18 (Show Source): You can put this solution on YOUR website!The annual yield per lemon tree is fairly constant at 320 pounds when the number of trees per acre is 50 or fewer. For each additional tree over 50, the annual yield per tree for all trees on the acre decreases by 4 pounds due to overcrowding. Find the number of trees that should be planted on an acre to produce the maximum yield. ; Let x = no. of trees, over 50, planted Then y = total yield per acre : total yield = No.of trees * lbs of lemons per tree : y = (50+x) * (320 - 4x) FOIL y = 16000 - 200x + 320x - 4x^2 The quadratic equation y = -4x^2 + 120x + 16000 : The axis of symmetry will be the value of x for max y The formula for that: x = In this problem: a=-4; b=120 x = x = x = +15 trees over 50 (65) gives max yield per acre : How many pounds is the maximum yield? : you can find that, substitute 15 for x in the quadratic equation
 Distributive-associative-commutative-properties/167065: A five digit number is represented by ABCDE where each letter represents a digit. If we add the digit 1 in front of ABCDE, we get 1ABCDE. The product of 1ABCDE and 3 is the six digit number ABCDE1. Find the value of the original number ABCDE1 solutions Answer 123337 by ankor@dixie-net.com(15657)   on 2008-11-13 14:29:32 (Show Source): You can put this solution on YOUR website!A five digit number is represented by ABCDE where each letter represents a digit. : If we add the digit 1 in front of ABCDE, we get 1ABCDE. The product of 1ABCDE and 3 is the six digit number ABCDE1. : Find the value of the original number ABCDE : Starting from the right, side we know that E=7 because it's the only number multiplied by 3 that will give last number as 1 : We have: 1ABCD7 X 3 ------ ABCD71; changed E to 7 here too : D = 5, multiplied 3, carry 2 to give us 17 we have 1ABC57 X 3 ------- ABC571; change D to 5 here too : C = 8, Multiplied by 3, carry 1 to give us 25 we have: 1AB857 X 3 -------- AB8571; change C to 8 : B = 2, Multiplied by 3, carry 2, to give us 8 we have: 1A2857 X 3 ------- A28571; change B to 2 : A = 4, multiplied by 3 gives 12 we have 142857 X 3 ----------- 428571 : ABCDE = 42857
 Travel_Word_Problems/167160: Roma Sherry drove 330 miles from her hometown to Tucson. During her return trip, she was able to increase her speed by 11 mph. If her return trip took 1 hour less time, find her original speed and her speed returning home.1 solutions Answer 123305 by ankor@dixie-net.com(15657)   on 2008-11-13 09:48:34 (Show Source): You can put this solution on YOUR website!Roma Sherry drove 330 miles from her hometown to Tucson. During her return trip, she was able to increase her speed by 11 mph. If her return trip took 1 hour less time, find her original speed and her speed returning home. : Let s = original speed then (s+11) = return speed : Write a time equation: Time = : Original time = return time + 1 hr = + 1 : Multiply equation by s(s+11) and you have: 330(s+11) = 330s + s(s+11) : 330s + 3630 = 330s + s^2 + 11s : 0 = 330s - 330s + s^2 + 11s - 3630 : A quadratic equation: s^2 + 11s - 3630 = 0 Factor this to: (s + 66)(s - 55) = 0 Positive solution s = 55 mph is original speed. : Find the time 330/55 = 6 hr, original time and 330/66 = 5 hrs, faster time; confirms our solution. :
 Signed-numbers/167390: Dear Tutor, I have a big proplem. I moved to Austia 2 years ago and i did not know german so i was not able to do the math. In school we are learning Pre algebra and i do not know a thing. if you can may you send me a couple of tipps and explainations to algebra Thank you!1 solutions Answer 123299 by ankor@dixie-net.com(15657)   on 2008-11-13 09:27:35 (Show Source): You can put this solution on YOUR website! have a big proplem. I moved to Austia 2 years ago and i did not know german so i was not able to do the math. In school we are learning Pre algebra and i do not know a thing. if you can may you send me a couple of tipps and explainations to algebra : My advice to you is get a used pre-algebra book (in English) on Amazon or Alibris they are very cheap. I have one (ISBN 0-395-74616-7) not too bad. Read, work the problems, if you need it, you can submit specific problems here and someone will explain it to you. The good thing is algebra is pretty much the same in any language.
 Money_Word_Problems/167378: Juan has a jar containing eighty coins, all of which are either quarters or nickels. The total value of the coins is \$14.60. How many of each type of coin does he have? Arbitrarily I tried 60 quarters, but that ended up \$15.00; then I dropped it to 55 quarters, which ended up \$13.75, but the remainng number of coins had to be 25 which would have brought the total to 80 coins (correct answer), but it equals \$15.85 which is too much.(You see, I've been working at it.) Question: is there a formula for this stuff? Thank you very much. 1 solutions Answer 123288 by ankor@dixie-net.com(15657)   on 2008-11-13 08:19:18 (Show Source): You can put this solution on YOUR website!Juan has a jar containing eighty coins, all of which are either quarters or nickels. The total value of the coins is \$14.60. How many of each type of coin does he have? : Actually it is quite simple using two equations: Let n = no. of nickels let q = no. of quarters ; Total coin equation n + q = 80 or n = (80-q) : Total value equation: .05n + .25q = 14.60 : From the 1st equation, substitute (80-q) for n .05(80-q) + .25q = 14.60 4 - .05q + .25q = 14.60 -.05q + .25q = 14.60 - 4 .20q = 10.60 q = q = 53 quarters : I'll let you find the no. of nickels
 Radicals/167316: sqrtof 9x+81=x+5 not sure how to solve...please help1 solutions Answer 123258 by ankor@dixie-net.com(15657)   on 2008-11-12 21:38:11 (Show Source): You can put this solution on YOUR website! = x + 5 Square both sides: 9x + 81 = (x + 5)^2 : FOIL the right side 9x + 81 = x^2 + 10x + 25 : 0 = x^2 + 10x - 9x + 25 - 81 : A quadratic equation: x^2 + x - 56 = 0 Factors to: (x+8)(x-7) = 0 Two solutions x = -8 and x = 7 : Both solutions have to be checked in the original equation: x= -8 = -8 + 5 = -8 + 5 = -3 3 does not = -3; x = -8 is not a solution : x=+7 = 7 + 5 = 12 = 12 12 = 12; x=7 is good solution
 Surface-area/167320: I have the total surface area, and I have two of the three dimensions given, how do I figure out the missing (third) dimension?1 solutions Answer 123245 by ankor@dixie-net.com(15657)   on 2008-11-12 21:02:50 (Show Source): You can put this solution on YOUR website!I have the total surface area, and I have two of the three dimensions given, how do I figure out the missing (third) dimension? : Look at the Surface area equation: Dimensions: L by W by H ; 2LW + 2LH + 2WH = SA : Let's say the missing dimension is L. Solve this equation for L : Subtract 2WH from both sides: 2LW + 2LH = SA - 2WH : Factor out L on the left L(2W + 2H) = SA - 2WH : Divide both side by (2W+2H) and you have: L = ; Substitute the other two dimensions (W & H) and the surface area to find L
 Linear-equations/167251: This question is from textbook Finite Mathematics with Aplications Can you help with this question on writing a cost function, assuming the relationship is linear: A cab company charges a base rate of 41.50 plus 15 cents per minute. Let C(x) be the cost in dollars of using the cab for x minutes. A. C(x)=1.50x+0.15 B. C(x)=1.50x-0.15 C. C(x)=0.15x-1.50 D. C(x)=0.15+1.501 solutions Answer 123234 by ankor@dixie-net.com(15657)   on 2008-11-12 20:05:20 (Show Source): You can put this solution on YOUR website!A cab company charges a base rate of 41.50 plus 15 cents per minute. Let C(x) be the cost in dollars of using the cab for x minutes. : That 41.50 must mean \$1.50 ; Cost = Cost for x miles + fixed cost C(x) = .15x + 1.50; it may be d and you forgot the x in there
 Average/167299: Average age of A & B is 24 years and average of B, C & D is 22 years. The sum of the ages A, B, C & D is 1 solutions Answer 123232 by ankor@dixie-net.com(15657)   on 2008-11-12 19:59:14 (Show Source): You can put this solution on YOUR website!Average age of A & B is 24 years, therefore their sum = 48 yrs : average of B, C & D is 22 years, therefore their sum = 66 yrs Assume B = 23 yrs old, : The sum of the ages A, B, C & D is: : Ensure that A + B add up to 48 Ensure that B + C + D add up to 66 : 25 + 23 + 22 + 21 = 91 : Assume that B = 25 yrs old then 23 + 25 + 20 + 21 = 89 ; I don't think there is a unique solution
 Functions/167250: This question is from textbook Algebra 1 Chanda is now four times old as her sister Suzane. Next year, Chanda's age will be three times Suzanne's age then. How old is each now?1 solutions Answer 123193 by ankor@dixie-net.com(15657)   on 2008-11-12 16:47:12 (Show Source): You can put this solution on YOUR website!Let C = Chanda's age now Let S = Suzanne's age now : Write an equation for each statement: : "Chanda is now four times old as her sister Suzanne." C = 4S ; "Next year, Chanda's age will be three times Suzanne's age then." C + 1 = 3(S + 1) : C + 1 = 3S + 3 : C = 3S + 3 - 1 : C = 3S + 2 : How old is each now? : From the 1st equation substitute 4S for C in the above equation 4S = 3S + 2 : 4S - 3S = 2 : S = 2 yrs is Suzanne's age now : You figure out C's age
 Complex_Numbers/167179: This question is from textbook beginning and intermediate algebra 13i\5+i i am very confused please help 1 solutions Answer 123188 by ankor@dixie-net.com(15657)   on 2008-11-12 16:35:17 (Show Source): You can put this solution on YOUR website!They probably want you to get rid of "i" in the denominator Multiply by the conjugate of (5+i) which is (5-i) over itself, (same as mult by 1) * : Multiply the numerators and FOIL the denominators. Remember i^2 = -1 = = = = + : Note that we can reduce both fractions, they both are multiples of 13 + = is the form they want probably ; Did this help?
 Polynomials-and-rational-expressions/167209: Polynomial Word Problem. A launched rocket has an altitude, in meters, given by the polynomial h+vt-4.92, where h is the height, in meters, from which the launce occurs, at velocity v in meters per second, a t is the number of seconds for which the rocket is airborne. If a rocket is launched from the top of a tower 50 meters high with an initial upward speed of 40 meters per second, what will its height be after 2 seconds? (round to the nearest tenth) 1 solutions Answer 123150 by ankor@dixie-net.com(15657)   on 2008-11-12 13:31:20 (Show Source): You can put this solution on YOUR website!A launched rocket has an altitude, in meters, given by the polynomial h+vt-4.92, where h is the height, in meters, from which the launce occurs, at velocity v in meters per second, a t is the number of seconds for which the rocket is airborne. If a rocket is launched from the top of a tower 50 meters high with an initial upward speed of 40 meters per second, what will its height be after 2 seconds? (round to the nearest tenth) : I think the equation would be: f(t) = -4.92t^2 + vt + h; where: f(t) = height in meters after t seconds -4.92t^2 = force of gravity pulling down : f(t) = -4.92t^2 + 40t + 50; equation for this problems : To find the height after 2 seconds, substitute 2 for t and and find f(t) f(t) = -4.92*2^2 40(2) + 50 : f(t) = -4.92*4 + 80 + 50 : f(t) = -19.68 + 130 : f(t) = 110.3 meters after 2 seconds
 Miscellaneous_Word_Problems/167130: This question is from textbook Algebra and Trigonometry Structure and Method book 2 I have been working on this math problem and I can't figure out how to get the answer. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Problem Solving Using Polynomial Equations Solve each problem. If there are two correct answers, give both of them. The area of a right triangle is 44m^2. Find the lengths of its legs if one of the legs is 3m longer than the other.1 solutions Answer 123104 by ankor@dixie-net.com(15657)   on 2008-11-11 21:48:38 (Show Source): You can put this solution on YOUR website!The area of a right triangle is 44m^2. Find the lengths of its legs if one of the legs is 3m longer than the other. : Let x = length of one leg, also the base (b) then (x+3) = length of the other leg. Also the height (h) : *b*h = Area In this problem *x*(x+3) = 44 Get rid of the fraction, multiply both sides by 2 x(x+3) = 88 : x^2 + 3x - 88 = 0; our old friend, the quadratic equation Factor this to: (x + 11)(x - 8) = 0 The positive solution: x = +8 : We don't consider the negative solution here. : Check solution by finding the area: A = .5(8*11) = 44
 Human-and-algebraic-language/166920: Algebra You are working with three different numbers. When the first number is added to twice the other two numbers, the result is 64 (x + 2y + 2z= 64). When the second number is added to twice the other two numbers the result is 62. Finally, when the third number is added to twice the other two numbers, the result is 59. what are the three numbers??1 solutions Answer 123102 by ankor@dixie-net.com(15657)   on 2008-11-11 21:36:02 (Show Source): You can put this solution on YOUR website!You are working with three different numbers. When the first number is added to twice the other two numbers, the result is 64 x + 2y + 2z = 64 ; When the second number is added to twice the other two numbers the result is 62. 2x + y + 2z = 62 : Finally, when the third number is added to twice the other two numbers, the result is 59. 2x + 2y + z = 59 : Using the 1st two equations x + 2y + 2z = 64 2x + y + 2z = 62 -------------------subtraction eliminates z -x + y = 2 y = x+2 : Multiply the 3rd equation by 2, and subtract the 1st equation 4x + 4y + 2z = 118 x + 2y + 2z = 64 -------------------subtraction eliminates z again 3x + 2y = 54 Substitute(x+2) for y 3x + 2(x+2) = 54 3x + 2x + 4 = 54 5x = 54 - 4 5x = 50 x = 10 is the 1st number then y = 10+2 y = 12 is the 2nd number : Find z using the 3rd equation 2(10) + 2(12) + z = 59 20 + 24 + z = 59 z = 59 - 44 z = 15 is the 3rd number : : Check solution in the 2nd equation 2(10) + 12 + 2(15) = 62 : what are the three numbers?? 10, 12, 15 :
 Quadratic_Equations/167122: x varies directly as the square of s and inversely as t. How does x change when s is doubled? When both s and t are doubled?1 solutions Answer 123101 by ankor@dixie-net.com(15657)   on 2008-11-11 21:11:30 (Show Source): You can put this solution on YOUR website!x varies directly as the square of s and inversely as t. H x = : How does x change when s is doubled? x = = ; x increase 4 times : : When both s and t are doubled? x = = = : We can say that x is doubled
 Travel_Word_Problems/167096: Mrs Dang drove her daughter to school at the average speed of 45 miles per hour. she returend home by the same route at the average speed of 30 miles per hour. if the trip took one half hour, how long did it take to get to school?, how far is the school from their home?1 solutions Answer 123099 by ankor@dixie-net.com(15657)   on 2008-11-11 21:00:30 (Show Source): You can put this solution on YOUR website!Mrs Dang drove her daughter to school at the average speed of 45 miles per hour. she returned home by the same route at the average speed of 30 miles per hour. if the trip took one half hour, how long did it take to get to school?, how far is the school from their home? : Let d = distance to the school : Write a time equation: Time = To school time + return time = half hour + = .5 Multiply equation by 90 to get rid of the denominators: 90* + 90* = 90(.5) cancel out the denominators; 2d + 3d = 45 : 5d = 45 d = d = 9 miles : Find the time to get to school (Time = dist/speed) 9/45 = .2 hr or .2(60) = 12 min : : Check solution find the time to return 9/30 = .3 hr or .3(60) = 18 min; (they add up to a half hr)
 Travel_Word_Problems/166998: A person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-forth greater, the person would have traveled only 1315 miles in the same length of time. Find the speeds of the plane and the ship. 1 solutions Answer 123070 by ankor@dixie-net.com(15657)   on 2008-11-11 18:40:35 (Show Source): You can put this solution on YOUR website!A person traveling 4 hr by plane and 25 hr by ship covers 1580 miles. If the speed of the plane had been one-half of the actual speed and the speed of the ship had been one-forth greater, the person would have traveled only 1315 miles in the same length of time. Find the speeds of the plane and the ship. : Let x = speed of plane and Let y = speed of shipe : Two distance equations; dist = time * speed : 4x + 25y = 1580 and 4(.5x) + 25(1.25y) = 1315 2x + 31.25y = 1315 : Multiply above equation by 2. Subtract the first equation 4x + 62.5y = 2630 4x + 25y = 1580 ---------------------subtraction eliminates x, find y: 37.5y = 1050 y = y = 28 mph speed of the ship : Find x using the 1st equation 4x + 25(28) = 1580 4x + 700 = 1580 4x = 1580 - 700 4x = 880 x = x = 220 mph speed of the plane : : Check solution in 2nd equation: 4(110) + 25(35) = 440 + 875 = 1315
 Length-and-distance/167025: The difference of the areas of two squares is 75 square feet. Each side of the larger square is twice the length of the smaller square. Find the length of a side of each square.1 solutions Answer 123031 by ankor@dixie-net.com(15657)   on 2008-11-11 16:05:06 (Show Source): You can put this solution on YOUR website!The difference of the areas of two squares is 75 square feet. Each side of the larger square is twice the length of the smaller square. Find the length of a side of each square. : Let x = length of the side of the smaller square then 2x = length of the side of the larger square : : Large sq area - small sq area = 75 sq/ft (2x)^2 - x^2 = 75 : 4x^2 - x^2 = 75 : 3x^2 = 75 x^2 = x^2 = 25 x = 5 ft side of the small square and 10 ft side of the large square : Check solution 10^2 - 5^2 = 75
 Miscellaneous_Word_Problems/167043: This question is from textbook Intermediate Algebra I have tried to figure out the equation to solve this problem. I have had friends help and together we could not find the anwser. I looked in the back to get the anwser and I can not figure out how to get the solution. I am trying to find out how many shares of each the pension fund owns. A pension fund owns 2,000 fewer shares in mutual stock than mutual bond funds. Currently, the stock funds sell for \$12 per share and the bonds sell for \$15 per share. How many shares of each does the pension fund own if the value of the securities is \$165,000.1 solutions Answer 123029 by ankor@dixie-net.com(15657)   on 2008-11-11 15:53:31 (Show Source): You can put this solution on YOUR website!A pension fund owns 2,000 fewer shares in mutual stock than mutual bond funds. Currently, the stock funds sell for \$12 per share and the bonds sell for \$15 per share. How many shares of each does the pension fund own if the value of the securities is \$165,000 : Let x = number of mutual bond fund share : It says mutual stock is 2000 fewer, so we can say: (x - 2000) = no. of mutual stock shares : A simple equation: Bond sh value + stock sh value = total value 15x + 12(x-2000) = 165000 : 15x + 12x - 24000 = 165000 : 27x = 165000 + 24000 : 27x = 189000 x = x = 7000 sh of mutual bond shares then 7000 - 2000 = 5000 sh of mutual stock shares : : Check our solutions: 15(7000) + 12(5000) = 105000 + 60000 = 165000
 Square-cubic-other-roots/167014: At a height of h meters you can see V kilometere to the hozizon These number are related by the equation V = 3.5 sqrt(h) A person can see 392 km to the horizon from an airplane window. How high is the airplane?1 solutions Answer 123027 by ankor@dixie-net.com(15657)   on 2008-11-11 15:38:52 (Show Source): You can put this solution on YOUR website!At a height of h meters you can see V kilometers to the horizon. These numbers are related by the equation V = 3.5 sqrt(h) A person can see 392 km to the horizon from an airplane window. How high is the airplane? : Substitute 392 for V in the given equation and find h 3.5* = 392 : Divide both sides by 3.5: = : = 112 : Square both sides: h = 112^2 : h = 12,544 meters : : Check solution on a calc: enter 3.5* = 392
 Numbers_Word_Problems/167005: The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more that five the old number. If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number,1 solutions Answer 123026 by ankor@dixie-net.com(15657)   on 2008-11-11 15:21:34 (Show Source): You can put this solution on YOUR website!I am going to re-write the problem to what I think you meant: : The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more than five times the old number. If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number, : Let the number be: 100x + 10y + z : Let's try solving this using only the 1st and last statements: "The sum of the digits of a three-digit number is 11." x + y + z = 11 : "the hundreds digit plus twice the tens digit is equal to the units digit," x + 2y = z x + 2y - z = 0 : Add to the 1st equation to eliminate z x + y + z = 11 x +2y - z = 0 -------------- 2x + 3y = 11 : 2x = 11 - 3y x = Only two values for y will give a positive integer value for x, namely 1 and 3: From the 2nd statement we know that x is a low value, therefore 3 seems likely: x = x = x = x = 1 when y = 3 Find z 1 + 3 + z = 11 z = 11-4 z = 7 ; Our number is 137 : See if that makes the 2nd statement true. "If the digits are reversed, the new number is 46 more than five times the old number" 731 = 5(137) + 46 731 = 685 + 46
 Age_Word_Problems/167013: The sum of the ages of four daughters, Abigail, Bonnie, Cena, and Daphne, is 40. The difference between the ages of the youngest, Daphne, and the oldest, Abigail, is 6. The second born, Bonnie, is 2 years younger than the oldest, Abigail, and the third born, Cena, is the average of the ages of the youngest, Daphne, and the second born, Bonnie. How old is the father, who is 30 years older than the youngest daughter?1 solutions Answer 123024 by ankor@dixie-net.com(15657)   on 2008-11-11 13:52:29 (Show Source): You can put this solution on YOUR website!Write an equation for each statement, we will try to get everything in terms of a : The sum of the ages of four daughters, Abigail, Bonnie, Cena, and Daphne, is 40. a + b + c + d = 40 : The difference between the ages of the youngest, Daphne, and the oldest, Abigail, is 6. a - d = 6 -d = 6 - a d = a - 6; multiplied equation by -1 : The second born, Bonnie, is 2 years younger than the oldest, Abigail, a - b = 2 -b = 2 - a b = a - 2 : third born, Cena, is the average of the ages of the youngest, Daphne, and the second born, Bonnie. c = Substitute (a-2) for b and (a-6) for d c = = Cancel out the denominator and we have: c = a - 4 : Substitute for b, c, d in the first equation, find a: a + (a-2) + (a-4) + (a-6) = 40 4a - 12 = 40 4a = 40 + 12 4a = 52 a = a = 13 yrs is Abigail's age Then b = 13 - 2 b = 11 yrs is Bonnie and c = 13 - 4 c = 9 yrs is Cena and d = 13 - 6 d = 7 yrs is Daphne : How old is the father, who is 30 years older than the youngest daughter? Father = 7 + 30 = 37 yrs old : : Check solution, find the total 13 + 11 + 9 + 7 = 40 : A lot of steps but not that hard, right?
 Graphs/166915: This question is from textbook Algebra 1 After visiting relatives who live 200 miles away, your family drives home at an average speed of 50 miles per hour. Your distance d (in miles) from home is given by d = 200 - 50t where t is the time (in hours) spent driving. Graph the function and identify its domain and range. What is your distance from home after driving for 1.5 hours?1 solutions Answer 123021 by ankor@dixie-net.com(15657)   on 2008-11-11 12:36:16 (Show Source): You can put this solution on YOUR website!After visiting relatives who live 200 miles away, your family drives home at an average speed of 50 miles per hour. Your distance d (in miles) from home is given by d = 200 - 50t where t is the time (in hours) spent driving. Graph the function and identify its domain and range. What is your distance from home after driving for 1.5 hours? : A graph of this: : You can see from the graph: Domain; 0 to +4 Range: 0 to +200 : What is your distance from home after driving for 1.5 hours? : You can estimate this from the graph, however find the exact solution: Substitute 1.5 for t in the equation: d = 200 - 50(1.5) d = 200 - 75 d = 125 mi in 1.5 hrs :