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 Unit_Conversion_Word_Problems/582944: You are trying to decide which of 2 cars to buy. An American made costs \$14,500 and has a consumption of 28 miles/gallon. The other is Japanese, costs \$21,700 and with a consumption of 19km/litre. If the cost of petrol is \$2.50 per gallon, estimate the number of miles you will need to drive the second car to compensate for the higher cost of the car. 1 solutions Answer 372407 by ankor@dixie-net.com(15628)   on 2012-03-06 19:57:46 (Show Source): You can put this solution on YOUR website!You are trying to decide which of 2 cars to buy. An American made costs \$14,500 and has a consumption of 28 miles/gallon. The other is Japanese, costs \$21,700 and with a consumption of 19km/litre. If the cost of petrol is \$2.50 per gallon, estimate the number of miles you will need to drive the second car to compensate for the higher cost of the car. : Change 19 km to mile .6214(19) = 11.8066 mi/liter Change to mi/gal 11.8066 * 3.785 = 44.688 = 44.7 mi/gal : Let m = no. of miles for the total cost of be the same : 2.50* + 14500 = 2.50* + 21700 .0893m + 14500 = .0559m + 21700 .0893m - .0559m = 21700 - 14500 .0334m = 7200 m = 7200/.0334 m = 215,569 mi for the total cost of each to be about the same : : See if that works out Acost = 2.50* + 14500 cost = \$33,747 : Jcost = 2.50* + 21700 cost = \$33.756 :
 Expressions-with-variables/582894: A plane that can normally travel at 250 mph in calm air is flying onto a headwind of 25 mph. How far can the plane fly in 3 hours?1 solutions Answer 372364 by ankor@dixie-net.com(15628)   on 2012-03-06 16:40:01 (Show Source): You can put this solution on YOUR website!A plane that can normally travel at 250 mph in calm air is flying onto a headwind of 25 mph. How far can the plane fly in 3 hours? : 3(250-25) = 675 mi
 Rational-functions/583032: a welder requires 25 hours to do a job. after the welder and an apprentice work on a job for 10 hours the wilder quits, the apprentice finishes the job in 17 hours. How long would it take the apprentice, working alone, to do the job 1 solutions Answer 372363 by ankor@dixie-net.com(15628)   on 2012-03-06 16:36:37 (Show Source): You can put this solution on YOUR website!a welder requires 25 hours to do a job. after the welder and an apprentice work on a job for 10 hours the wilder quits, the apprentice finishes the job in 17 hours. How long would it take the apprentice, working alone, to do the job : Let a = time required by the apprentice to do the job Let the completed job = 1 : From the information given, we see the apprentice worked a total of 27 hrs : + = 1 multiply by 25a, results 10a + 25(27) = 25a 10a + 675 = 25a 675 = 25a - 10a 675 = 15a a = a = 45 hrs, the apprentice working alone
 Numbers_Word_Problems/582889: The sum of the 3 digits of an even number is 9. What is the number if its ten digits its 1 more than its ones digit?1 solutions Answer 372360 by ankor@dixie-net.com(15628)   on 2012-03-06 16:21:02 (Show Source): You can put this solution on YOUR website!The sum of the 3 digits of an even number is 9. What is the number if its ten digits its 1 more than its ones digit? : Three digits, a, b, c : a + b + c = 9 : b = c + 1 : a + (c+1) + c = 9 a + 2c = 9 - 1 a + 2c = 8 a = -2c + 8 : 3 solutions 621 432; the only even number 243
 Systems-of-equations/582863: 8/35x=-32/631 solutions Answer 372333 by ankor@dixie-net.com(15628)   on 2012-03-06 14:27:54 (Show Source): You can put this solution on YOUR website!8/35x=-32/63 is x part of the denominator, or do you mean: x =
 Age_Word_Problems/582942: Tom is 3 times as old as his cousin Sam and 14 years older than his parrot Polly. In 4 years, Lucy will be half as old as Polly. How old is Tom ??1 solutions Answer 372316 by ankor@dixie-net.com(15628)   on 2012-03-06 13:28:51 (Show Source): You can put this solution on YOUR website!Tom is 3 times as old as his cousin Sam and 14 years older than his parrot Polly. In 4 years, Lucy will be half as old as Polly. How old is Tom ?? : Let t = Tom's age Let s = Sam's age Let p = parrot's age Let L = Lucy's age ; Write an equation for each statement:; : "Tom is 3 times as old as his cousin Sam" t = 3s ; " and 14 years older than his parrot Polly." t = p + 14 : "In 4 years, Lucy will be half as old as Polly." L + 4 = .5(p+4) L + 4 = .5p + 2 L = .5p + 2 - 4 L = .5p - 2 : How old is Tom ?? : A lot of unrelated facts here, all we know for sure is Tom is at least 15 years old and his age is multiple of 3, the parrot is an even number of years old in order for Lucy to be half it's age : Let's say Tom is 24, then Sam is 8, parrot is 10, Find Lucy's age L + 4 = .5(10+4) L + 4 = 7 L = 7 - 4 Lucy is 3 ; Tom is 24 is one answer
 Linear_Equations_And_Systems_Word_Problems/582880: need to come up with two equations, with x and y A bricklayer lays an average of 150 bricks per hour. During a job, he is called away and replaced by a less experienced man, who averages 120 bricks per hour. The two men laid 930 bricks in 7 hours. How long did each work?1 solutions Answer 372270 by ankor@dixie-net.com(15628)   on 2012-03-06 08:31:32 (Show Source): You can put this solution on YOUR website!A bricklayer lays an average of 150 bricks per hour. During a job, he is called away and replaced by a less experienced man, who averages 120 bricks per hour. The two men laid 930 bricks in 7 hours. How long did each work? : Let x = time worked by the experienced bricklayer Let y = time worked by apprentice : Time equation x + y = 7 y = (7-x); use this form for substitution : Production equation 150x + 120y = 930 replace y with (7-x), find x 150x + 120(7-x) = 930 150x + 840 - 120x = 930 150x - 120x = 930 - 840 30x = 90 x = 90/30 x = 3 hrs worked the exp guy : You can find the hrs worked by the other guy. check solutions in the production equation
 Miscellaneous_Word_Problems/582407: The cabels of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 400 feet apart and 100 feet high. If the cables are at the height of 10 feet ,idway between the towers, what is the height of the cable at the point 50 feet from the center of the bridge?1 solutions Answer 372240 by ankor@dixie-net.com(15628)   on 2012-03-05 21:55:25 (Show Source): You can put this solution on YOUR website!The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 400 feet apart and 100 feet high. If the cables are at the height of 10 feet midway between the towers, what is the height of the cable at the point 50 feet from the center of the bridge? : Use the given information to create a quadratic equation to represent this bridge Using the form: ax^2 + bx + c = y left side x=0, y=100, therefore c=100 : Midway x=200, y=10 200^2a + 200b + 100 = 10 40000a + 200b = 10 - 100 40000a + 200b = -90 : right end x=400, y=100 400^2a + 400b + 100 = 100 160000a + 400b = 0 : Multiply the midway equation by 2, subtract from the above 160000a + 400b = 0 80000a + 400b = -180 -----------------------subtraction eliminates b, find a 80000a = 180 a = 180/80000 a = .00225 find b 160000(.00225) + 400b = 0 360 + 400b = 0 400b = -360 b = -360/400 b = -.9 : The equation: y = .00225x^2 - .9x + 100 looks like this : "what is the height of the cable at the point 50 feet from the center of the bridge?" x = 200-50 x = 150 y = .00225(150^2) - .9(150) + 100 y = 15.625 ft above 0 : x = 200 + 50 x = 250 do the same as we did above
 Travel_Word_Problems/582322: If it takes 2hrs and 30mins to encode 300pages. How many minutes will it take to encode 1 page?1 solutions Answer 372232 by ankor@dixie-net.com(15628)   on 2012-03-05 21:26:50 (Show Source): You can put this solution on YOUR website!If it takes 2hrs and 30mins to encode 300pages. Convert 2 hr 30 min to 150 minutes How many minutes will it take to encode 1 page? = min per page
 Travel_Word_Problems/582554: It takes Sally three minutes to go one mile with the wind at her back. Then it takes her four minutes on the ride back with the wind against her. What is the rate of the speed of the wind? Please help me. I tried this and got the answer of one over twentyfour.1 solutions Answer 372230 by ankor@dixie-net.com(15628)   on 2012-03-05 21:17:08 (Show Source): You can put this solution on YOUR website!It takes Sally three minutes to go one mile with the wind at her back. Then it takes her four minutes on the ride back with the wind against her. What is the rate of the speed of the wind? : Assume they want the speeds in mph : Convert 1 mi in 3 min to mph = 20 mph effective speed with the wind and = 15 mph effective speed against the wind : Let s = speed in still air Let w = speed of the wind : s + w = 20 s - w = 15 -----------adding eliminates w, find s 2s = 35 s = 35/2 s = 17.5 mph in still air : Find the speed of the wind 17.5 + w = 20 w = 20 - 17.5 w = 2.5 mph is the rate of the wind
 Expressions-with-variables/582398: please help me to grasp the concept of solving with elimination method. -3x+4y=1 -6+6y=-3 4x-8y=48 11x+3y=105.5 8x+11y=-50 -32x-44y=-2001 solutions Answer 372204 by ankor@dixie-net.com(15628)   on 2012-03-05 20:02:51 (Show Source): You can put this solution on YOUR website!solving with elimination method. -3x + 4y = 1 -6x + 6y =-3 the idea is to multiply one or both equations so that one variable has the same coefficient, ideally one is positive and the other negative Multiply the 1st equation by -2, add to the 2nd equation +6x - 8y = -2 -6x + 6y = -3 ----------------Adding eliminates x, find y 0 + -2y = -5 y = y = +2.5 ; find x using the 1st equation -3x + 4(2.5) = 1 -3x + 10 = 1 -3x = 1 - 10 -3x = -9 divide both sides by -3 x = 3 : Check our solution in the 2nd equation -6x + 6y = -3 -6(3) + 6(2.5) = -3 -18 + 15 = -3 : : 4x - 8y = 48 11x + 3y = 105.5 multiply the 1st equation by 3, the 2nd equation by 8 12x - 24y = 144 88x + 24y = 844 -----------------adding eliminates y, find x 100x + 0 = 988 x = 988/100 x = 9.88 : Find y using the 1st equation 4(9.88) - 8y = 48 39.52 - 8y = 48 -8y = 48 - 39.52 -8y = 8.48 y = y = -1.06 : Check solution in the 2nd equation 11x + 3y = 105.5 11(9.88) + 3(-1.06) = 105.5 108.68 - 3.18 = 105.5 : : 8x + 11y = -50 -32x -44y =-200 multiply the 1st equation by 4, add to the 2nd equation +32x + 44y = -200 -32x -44y = -200 -------------- note that every term cancels, the two equations are equivalent, dependent
 Geometry_Word_Problems/582370: I have bee trying to figure this problem out for hours. Please help. From 2005 to 2007, enrollment at a university decreased by 2%. If enrollment in 2007 was 8771 students, what was the enrollment in 2005?1 solutions Answer 372127 by ankor@dixie-net.com(15628)   on 2012-03-05 18:16:44 (Show Source): You can put this solution on YOUR website!From 2005 to 2007, enrollment at a university decreased by 2%. If enrollment in 2007 was 8771 students, what was the enrollment in 2005? : Let x = enrollment in 2005 the multiplier for 2% drop is .98 : This occurred for 2 yrs so we have: : x*.98^2 = 8771 x * .9604 x = x = 9,133 students in 2005
 Trigonometry-basics/582488: Can you please exlpain step by step how to solve 2/x-3 - 4/x+3 = 8/x^2-91 solutions Answer 372102 by ankor@dixie-net.com(15628)   on 2012-03-05 17:25:57 (Show Source): You can put this solution on YOUR website! = The third denominator is the difference of squares and can be factored to; = Multiply each term by (x-3)(x+3) (x-3)(x+3)* - (x-3)(x+3)* = (x-3)(x+3)* Cancel the denominators and you have: 2(x+3) - 4(x-3) = 8 2x + 6 - 4x + 12 = 8 2x - 4x + 18 = 8 -2x = 8 - 18 -2x = -10 x = +5 : : Check this in the original problem for x = 5 =
 Travel_Word_Problems/582282: You drive to your Nana’s at a speed of 20 km/h and then come home at a speed to 30 km/h. What is the average speed for the whole trip?1 solutions Answer 372076 by ankor@dixie-net.com(15628)   on 2012-03-05 16:06:12 (Show Source): You can put this solution on YOUR website!You drive to your Nana’s at a speed of 20 km/h and then come home at a speed to 30 km/h. What is the average speed for the whole trip? : Let a = average speed for the whole trip : let d = distance one way then 2d = distance for the whole trip : write a time equation; time = dist/speed : there time + return time = total time + = multiply by 60a 60a* + 60a* = 60a cancel the denominator, results: 3ad + 2ad = 60(2d) 5ad = 120d Divide both side by d 5a = 120 a = 120/5 a = 24 mph average speed for the whole trip
 Rate-of-work-word-problems/582315: if 3 men can repair the house in 20 days,how many days can 5 men do the same job?1 solutions Answer 372068 by ankor@dixie-net.com(15628)   on 2012-03-05 14:27:49 (Show Source): You can put this solution on YOUR website!if 3 men can repair the house in 20 days, how many days can 5 men do the same job? : Find how many man-days to complete the job. 3*20 = 60 man-days : " how many days can 5 men do the same job?" let d = no. of days required by 5 men to do it 5d = 60 d = 60/5 d = 12 days
 Linear-equations/582345: Find the equation of the line that contains the point (4,-2). and has slope 3/4. I started with using the formula y=mx+b. I set it up as -2=3/4 (4)+b but I can't finish it from here.1 solutions Answer 372066 by ankor@dixie-net.com(15628)   on 2012-03-05 14:19:21 (Show Source): You can put this solution on YOUR website!Find the equation of the line that contains the point (4,-2). and has slope 3/4. : mx + b = y Replace m, x, y (4) + b = -2 3 + b = - 2 b = - 2 - 3 b = -5 : y = x - 5 is the equation : You can check this, replace x with 4, in the equation and see if y = -2
 Travel_Word_Problems/582213: After about 8 hours of a steady wind, the height (y) of waves in the ocean is linearly related to the duration of time (x) the wind has been blowing. During a storm with 40-knot winds, the wave height after 8 hours was found to be 22 feet, and after 23 hours it was 41 feet. (a) Write a linear equation that relates the height to time. (b) How long will the wind have been blowing for the waves to be 60 feet heigh?1 solutions Answer 372058 by ankor@dixie-net.com(15628)   on 2012-03-05 13:30:15 (Show Source): You can put this solution on YOUR website!After about 8 hours of a steady wind, the height (y) of waves in the ocean is linearly related to the duration of time (x) the wind has been blowing. During a storm with 40-knot winds, the wave height after 8 hours was found to be 22 feet, and after 23 hours it was 41 feet. : (a) Write a linear equation that relates the height to time. find the slope: m = assign the values as follow x1=8, y1=22 x2=23, y2=41 : Find the slope (m) m = = = is the slope : Use the point/slope form to create an equation: y - y1 = m(x - x1) y - 22 = (x - 8) y - 22 = x - y = x - + 22 y = x - + y = x + ; is the equation : (b) How long will the wind have been blowing for the waves to be 60 feet height? x + = 60 multiply by 15 to get rid of the denominators 19x + 178 = 15(60) 19x = 900 - 178 19x = 722 x = x = 38 hrs to reach 60 ft waves
 Percentage-and-ratio-word-problems/582334: A motorcycle breaks down and the rider must walk the rest of the way to work. The motorcycle was being driven at 45mph, and the rider walks at a speed of 6mph. The distance from home to work is 25miles, and the time for the trip was 2hr. How far did the motorcyle go before it broke down?1 solutions Answer 372032 by ankor@dixie-net.com(15628)   on 2012-03-05 08:29:36 (Show Source): You can put this solution on YOUR website!A motorcycle breaks down and the rider must walk the rest of the way to work. The motorcycle was being driven at 45mph, and the rider walks at a speed of 6mph. The distance from home to work is 25miles, and the time for the trip was 2hr. How far did the motorcycle go before it broke down? : Let m = distance rode on the motorcycle then (25-m) = distance he walked : Write a time equation: time = dist/speed : ride time + walk time = 2 hrs + = 2 multiply by LCM of the denominators, 90 will do it, results: 2m + 15(25-m) = 90(2) : 2m + 375 - 15m = 180 2m - 15 m = 180 - 375 -13m = -195 13m = 195 m = 195/13 m = 15 mi on the motorcycle : : Check this by finding the actual times 15/45 = .33 10/6 = 1.67 ------------ tot time: 2 hrs
 Polynomials-and-rational-expressions/582207: Bob’s Barber Shop estimates their gross revenue for the second quarter to be given by the polynomial 7x3 + 6x2 – 6x – 3. The shop estimates their costs for that quarter to be given by 6x2 – 9x + 9. For the second quarter, find and simplify a polynomial that will represent their profit.1 solutions Answer 372031 by ankor@dixie-net.com(15628)   on 2012-03-05 08:16:09 (Show Source): You can put this solution on YOUR website!Bob’s Barber Shop estimates their gross revenue for the second quarter to be given by the polynomial 7x3 + 6x2 – 6x – 3. The shop estimates their costs for that quarter to be given by 6x2 – 9x + 9. For the second quarter, find and simplify a polynomial that will represent their profit. : Revenue: r(x) = 7x^3 + 6x^2 - 6x - 3 Costs: c(x) = 6x^2 - 9x + 9 : Profit (p) = Revenue - cost, therefore: p(x) = (7x^3 + 6x^2 - 6x - 3) - (6x^2 - 9x + 9) removing the brackets p(x) = 7x^3 + 6x^2 - 6x - 3 - 6x^2 + 9x - 9 combine like terms p(x) = 7x^3 + 6x^2 - 6x^2 - 6x + 9x - 3 - 9 : p(x) = 7x^3 + 3x - 12; is the profit
 Exponents/582199: im so confused!! im in grade 10 foundations math and were working on rational exponents. is the question is to evaluate 16 & 3/4 i change it too the square root of 16 to the power of 3 and then the four goes on the left hand side outside of the square root symbol. i get 64 but then i dont know what to do with the four. do i divide 64 by four? it wasnt expained...1 solutions Answer 371996 by ankor@dixie-net.com(15628)   on 2012-03-04 21:52:20 (Show Source): You can put this solution on YOUR website!16^(3/4) find the 4th root of 16, that is 2, right then 2^3 which is 8 : You can do it the other way too, but will need a calc find 16^3 = 4096 then find the 4th root of 4096, on a calc = 8 also
 Age_Word_Problems/581574: The sum of the ages of Mr. Smith, Ms. Smith and their son, Tommy Smith, is 74. Ten years ago, this sum was 47. How old is Ms. Smith now if Mr. Smith is 28 years older than Tommy? can you explain and show how you did the problem? thanks1 solutions Answer 371993 by ankor@dixie-net.com(15628)   on 2012-03-04 21:43:28 (Show Source): You can put this solution on YOUR website!Write an equation for each statement: : The sum of the ages of Mr. Smith, Ms. Smith and their son, Tommy Smith, is 74. a + b + c = 74 : Ten years ago, this sum was 47. (a-10) + (b-10) + (c-10) = 47 a + b + c - 30 = 47 a + b + c = 47 + 30 a + b + c = 77, but how could this be when above the sum is 74
 Exponents/581597: Using the exponential correlation, how do I solve for x. Round to three decimal places. 1)log(4x+10)=3 2)1/2 log6 16x +5=8 3)In(x+4)=-21 solutions Answer 371991 by ankor@dixie-net.com(15628)   on 2012-03-04 21:29:04 (Show Source): You can put this solution on YOUR website!1)log(4x+10)=3 the exponent equiv of logs 4x + 10 = 10^3 4x + 10 = 1000 4x = 1000 - 10 4x = 990 x = 990/4 x = 247.5 : 2)1/2 log6 16x +5 = 8 not sure what you mean here, but will assume this log6(16x) = 8 - 5 log6(16x) = 3 multiply both sides by 2 log6(16x) = 6 16x = 16x = 46656 x = 46656/16 x = 2916 : 3)In(x+4) = -2 x + 4 = e^-2 x + 4 = .1353 x = .1353 - 4 x = -3.864
 Rectangles/581883: The problem is, "The length of a rectangle exceeds it's width by 3 meters. The perimeter is 58 meters. Find the dimensions." I tried using subsitutions, but I got stuck and didn't get an answer. What do I do?1 solutions Answer 371990 by ankor@dixie-net.com(15628)   on 2012-03-04 21:11:48 (Show Source): You can put this solution on YOUR website!"The length of a rectangle exceeds it's width by 3 meters. The perimeter is 58 meters. Find the dimensions." : The perimeter: 2L + 2W = 58 We can simplify this, divide by 2, and you have L + W = 29 : We know: L = (W+3) : (W+3) + W = 29 2W = 29 - 3 2W = 26 W = 13 is the width then 13 + 3 = 16 is the Length ; Now you check this in the perimeter equation