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 Money_Word_Problems/566687: a door breaks down 7 times per hour. cost of idle door time is \$30 per hour. two carpenters Bob and Bill submit quotes to maintain the doors in the house. Bob charges \$21 per hour and can fix 10 doors per hour while Bill charges \$27 and can fix 13 doors per hour. Whose services should be employed?1 solutions Answer 366315 by Theo(3504)   on 2012-02-02 09:47:39 (Show Source): You can put this solution on YOUR website!door breaks down 7 times an hour and idle time on the door is 30 dollars per hour. 30 dollars per hour idle time equates to 30/60 = .5 dollars per minute. bob can fix 10 doors an hour. it takes him 60/10 = 6 minutes per door. bill can fix 13 doors an hour. it takes him 60/13 = 4.615384615 minutes per door. since the door breaks down 7 times an hour, then: with bob, the total down time per hour would be 7 * 6 = 42 minutes at a cost of .5 dollars per minute for a cost of 21 dollars per hour. with bill, the total down time per hour would be 7 * 4.615384615 = 32.30769231 minutes at a cost of .5 dollars per minute for a cost of 16.15384615 dollars per hour. total cost to the company for bob equals 21 + 21 = 42 dollars per hour. total cost to the company for bill equals 27 + 16.15384615 = 43.15384615 per hour. it's close, but as long as the door doesn't break down more than 7 times per hour, bob is the cheaper choice. the equation for the total cost with bob is: y = 21 + .5 * 6 * x the equation for the total cost with bill is: y = 27 + .5 * 4.615384615 * x thee lines will intersect when x = 8.6666667 for a cost of 47 per hour. when x is less than 8.6666667, bob is cheaper. when x is greater than 8.6666667, bill is cheaper. the graph is shown below: the line that intersects the y-axis at 27 is bill's equation. the line that intersects the y-axis at 21 is bob's equation. the horizontal line at y = 47 shows where the break even point is.
 Probability-and-statistics/566685: From experience, Teton Tire knows the probability is .95 that a particular XB-70 tire will last 60,000 miles before it becomes bald or fails. An adjustment is made on any tire that does not last 60,000 miles. You purchase 4 XB-70’s. a. (10 pts) What is the probability that all 4 tires will last at least 60,000 miles? b. (10 pts) What is the probability that none of the tires will last at least 60,000 miles? 1 solutions Answer 366312 by Theo(3504)   on 2012-02-02 09:01:28 (Show Source): You can put this solution on YOUR website!probability that all 4 tires will last at least 60,000 miles is .95^4 = .81450625 probability that all 4 tires will not last at least 60,000 miles is 1 - .81450625 = .18549375 probability that none of the tires will last at least 60,000 miles is .05^4 = 6.25 * 10^-6 the total probabilities are shown below: p(4 last 60,000) = 4C0 * .95^4 * .05^0 = 1 * .95^4 * .05^0 = .81450625 p(3 last 60,000) = 4C1 * .95^3 * .05^1 = 4 * .95^3 * .05^1 = .l71475 p(2 last 60,000) = 4C2 * .95^2 * .05^2 = 6 * .95^2 * .05^2 = .0135375 P(1 last 60,000) = 4C3 * .95^1 * .05^3 = 4 * .95^1 * .05^3 = 4.75 * 10^-4 p(0 last 60,000) - 4C4 * .95^0 * .05^4 = 1 * .95^0 * .05^4 = 6.25 * 10^-6 add all these probabilities together and you get a total probability of 1. the probability that 4 last 60,000 is.81450625. the probability that 0 last 60,000 is 6.25 * 10^-6. the probability that 4 do not last 60,000 is equal to 1 - .81450625 = .18549375. this is the probability that 0 and 1 and 2 and 3 last 60,000 which is the total probability minus the probability that 4 last 60,000 miles. you were asked: a. (10 pts) What is the probability that all 4 tires will last at least 60,000 miles? answer is.81450625 b. (10 pts) What is the probability that none of the tires will last at least 60,000 miles? answer is 6.25 * 10^-6 which is equivalent to .00000625
 test/566554: Im having trouble on the addition method1 solutions Answer 366294 by Theo(3504)   on 2012-02-02 03:18:18 (Show Source): You can put this solution on YOUR website!what kind of trouble? are you talking about solving equations simultaneously though the addition method? give me one of your problems and i'll show you how to solve it.
 Probability-and-statistics/566612: There are 7 men and 3 women in a room. Two of these 10 people are selected at random. If both people are the same gender, then what is the probability that they are both women?1 solutions Answer 366293 by Theo(3504)   on 2012-02-02 03:06:36 (Show Source): You can put this solution on YOUR website!7 men and 3 women. 2 selected at random. both are the same gender. let p(a) be the probability that they are both women. let p(b) be the probability that they are both the same gender. the probability that they are both men is 7/10 * 6/9 = 42/90 the probability that they are both women is 3/10 * 2/9 = 6/90 the probability that they are the same gender is equal to 42/90 + 6/90 = 48/90. the probability that they are the same sex and are both women at the same time is the same as the probability that they are both women. the formula for conditional probability is: p(a|b) = p(a^b)/p(b) this formula means: probability of a given b equals the probability of a and b occurring at the same time divided by the probability of b. probability of a and b occurring at the same time is the probability that they are the same gender and are both women at the same time which is equal to 6/90. the probability of b occurring is the probability that they are both of the same gender which is equal to 48/90. p(a|b) = p(a^b)/p(b) becomes: p(a|b) = (6/90) / (48/90) = (6/90) * (90/48) = 6/48 = .125 this might be easier to see in a smaller problem. assume 5 people and 2 are picked at random. 3 are men and 2 are women. probability that 2 people picked will be men is 3/5 * 2/4 = 6/20. probability that 2 people picked will be women is 2/5 * 1/4 = 2/20. probability that 2 people picked will be the same gender is equal to 6/20 + 2/20 = 8/20. probability that 2 people picked will be the same gender and will be women at the same time is equal to 2/20 which is the same as the probability that 2 women picked will be both women. probability that 2 people picked will be 2 women given that the people picked are the same gender is equal to probability they are the same gender and they are both women at the same time divided by the probability they are both of the same gender. this becomes (2/20) / (8/20) which equals (2/30) * (20/8) which is equal to (2/8) which i equal to .25. there is a .25 probability that, if the 2 people picked are the same gender, that they will be women. with 5 people, it's easier to show you how it works rather than with 10. here's the breakdown. assume men are numbers 1, 2, and 3 assume women are letters a and b. the possible 2 person combinations are: 1,2 *** 1,3 *** 1,a 1,b 2,3 *** 2,a 2,b 3,a 3,b a,b *** the persons of the same gender have an asterisk next to their selection. there are 4 out of 10 possible selections that are the same gender. out of these 4, 1 is both women. the probability that, given they are the same gender, that they will both be women is equal to 1 pair of women out of 4 total possible pairs of same gender. the same formula applies to 10 people where 7 are men and 3 are women as shown above.
 Travel_Word_Problems/566607: A family has two cars. The first car has a fuel efficiency of miles per gallon of gas and the second has a fuel efficiency of miles per gallon of gas. During one particular week, the two cars went a combined total of miles, for a total gas consumption of gallons. How many gallons were consumed by each of the two cars that week?1 solutions Answer 366289 by Theo(3504)   on 2012-02-02 02:06:13 (Show Source): You can put this solution on YOUR website!your formula is: bx + a(m-x) = abm/c a = miles per gallon of the first car. b = miles per gallon of the second car. c = combined mileage of both cars. m = total miles traveled by both cars. x = total miles traveled by first car. m-x = total miles traveled by second car. number of combined gallons consumed is equal to m/c number of gallons consumed by first car is x/a number of gallons consumed by second car is (m-x)/b let's see how it works. assume both cars traveled 1500 miles. assume first car gets 20 miles per gallon. assume second car gets 35 miles per gallon. assume the combined mileage is 25 miles per gallon. you want to know how many gallons was consumed by first car and how many gallons was consumed by second car. the formula is: bx + a(m-x) = abm/c you are given: a = 20 b = 35 c = 25 m = 1500 substitute in the equation to get: 35x + 20(1500-x) = 20*35*1500/25 simplify this equation to get: 35x + 30000 - 20x = 42000 combine like terms to get: 15x + 30000 = 42000 subtract 30000 from both sides of this equation to get: 15x = 42000 - 30000 simplify to get: 15x = 12000 divide both sides of this equation by 15 to get: x = 800 since m = 1500 and x = 800, this means that: m-x = 700 you now have: x = 800 m-x = 700 x is the number of miles traveled by the first car. m-x is the number of miles traveled by the second car. the number of gallons consumed by the first car is x/a which is equal to 800/20 which is equal to 40. the number of gallons consumed by the second car is (m-x)/b which is equal to 700/35 which is equal to 20. total gallons consumed by both cars is 40 + 20 = 60. both cars traveled 1500 miles total at a combined efficiency of 25 miles per gallon. combined gallons consumed is equal to m/c which is equal to 1500/25 which is equal to 60 gallons. the calculations for gallons consumed are the same so the values for x and m-x must be good. the formula works for any combined miles and combined miles per gallon as long as you know the miles per gallon of the first car and the miles per gallon of the second car as well.
 Inequalities/566608: how do I solve to get the inequality when: 2x+4> 1/3 1 solutions Answer 366288 by Theo(3504)   on 2012-02-02 01:10:28 (Show Source): You can put this solution on YOUR website!2x + 4 > 1/3 subtract 4 from both sides of the equation to get: 2x > 1/3 - 4 multiply 4 by 3/3 to get: 2x > 1/3 - 12/3 simplify to get: 2x > -11/3 divide both sides of the equation by 2 to get: x > -11/(3*2) simplify to get: x > -11/6 since this can't be simplified any further, that' your answer. confirm by substituting for x in your original equation. pick a value of x > -11/6 pick a value for x that is greater than -11/6. try -10/6 your original equation is: 2x + 4 > 1/3 substitute -10/6 for x to get: 2 * (-10/6) + 4 > 1/3 simplify to get: -20/6 + 4 > 1/3 multiply 4 by 6/6 to get: -20/6 + 24/6 > 1/3 combine like terms to get: 4/6 > 1/3 simplify to get: 2/3 > 1/3 since this equation is true, your value for x is probably good. to make a complete test, you would need to test out when x = -11/6 and when x < -11/6. both those tests should lead to a false equation (one that is not true). for example: when x = -11/6, the original equation of: 2x + 4 > 1/3 becomes: 2 * (-11/6) + 4 > 1/3 simplify to get: -22/6 + 4 > 1/3 multiply 4 by 6/6 to get: -22/6 + 24/6 > 1/3 combine like terms to get: 2/6 > 1/3 simplify to get: 1/3 > 1/3 this equation is false because 1/3 is equal to 1/3 and not greater than it. the value of x = -11/6 is not valid. this is correct because the solution to the equation said that x > -11/6, not x = to -11/6 and not x >= -11/6.
 Pythagorean-theorem/565306: using pythagorean theorem: how do i solve using a square root as one of the sides? for example: a^2=26 b^2=(square root 596) c^2=? 1 solutions Answer 365769 by Theo(3504)   on 2012-01-31 04:44:34 (Show Source): You can put this solution on YOUR website!the square root of 596 squared is equal to 596. the square root of anything squared is anything. example: the square root of 4^2 = 4 the square root of 6^2 = 6 you can prove this for yourself by squaring 4 and squaring 6 you get 16 and 36 square root of 16 = 4 square root of 36 = 6 in your problem you want to take the square root of 596^2. that equals 596. if you use your calculator and square 596 you'll get 355216 if you use your calculator and take the square root of 355216 you'll get 596.
 Functions/565316: Reading "50 Mathematical Ideas you really need to know". It gives Galileo's distance formula - y = 16 times x squared. It says the factor 16 is because feet and seconds are the chosen measurement units. Don't understand why 16? This is the introduction to Calculus and I haven't got past this number 16 yet. Thank you, Chris.1 solutions Answer 365768 by Theo(3504)   on 2012-01-31 04:37:31 (Show Source): You can put this solution on YOUR website!the formula is 16 * x^2 because the measurement was done in feet and seconds. if the measurement was done in some other measure, like inches in half a second intervals, the factors would have been different. the more generalized formula would be: d = k * x^2 where: k is the distance the object falls in 1 unit of time. x is the unit of time. for example: assume the distance was in inches and the time in seconds. the formula would then have become: d = (16*12 = 192) * x^2 where: 192 is the distance in inches and x is the number of seconds. assume the distance was in feet and the time interval was half a second. the formula would then have become: d = 4 * x^2 where: 4 is the number of feet the object fell in half a second and x is the number of half seconds. the formula works the same either way. the following chart should demonstrate that. a is from the equation d = 16 * x^2 where 16 is the the number of feet in 1 second and x is the number of seconds. b is from the equation d = 192 * x^2 where 192 is the number of inches in 1 second and x is the number of seconds. c is from the equation d = 4 * x^2 where 4 is the number of feet in half a second and x is the number of half seconds. seconds half seconds a b c 1 2 16 192 16 2 4 64 768 64 3 6 144 1728 144 15 30 3600 43200 3600 note that the results are the same regardless of the units used as long as you did the conversions correctly. 3600 feet * 12 inches per foot equals 43200 inches. 16 * 15^2 = 3600 4 * 30^2 = 3600 the formula is valid regardless of the units used. the reason why the formula you are looking at is d = 16 * x^2 where 16 is the number of feet it dropped in 1 second and x is the number of seconds is because those are the units of measure that were used in galileo's observation. from what i read, he may have actually used meters. the formula would have been d = 4.9 * x^2 where 4.9 is the number of meters in 1 second. 4.9 meters is roughly equivalent to 16 feet which is why you see 16 feet.
 Probability-and-statistics/565349: The probabilities that the serviceability of a new laser printer will be rated very difficult, difficult, average, easy or very easy are 0.11, 0.16, 0.35, 0.28, 0.10 respectively. Find the probability that the serviceability of a new laser printer will be rated (i) difficult or very difficult. (ii) difficult, average or easy. and (iii) average or better.1 solutions Answer 365767 by Theo(3504)   on 2012-01-31 03:34:20 (Show Source): You can put this solution on YOUR website!probabilities for service ratings are: very difficult .11 difficult .16 average .35 easy .28 very easy .10 presumably these ratings are independent of each other, i.e. a laser printer can be difficult to service or it can be easy to service but it can't be both at the same time. this makes p(a or b) equal to p(a) + p(b) if they were not independent of each other, then p(a or b) would be equal to p(a) + p(b) - p(a and b) as you may know, p(a and b) is equal to p(a) * p(b). if you don't yet, you will soon enough. anyway, assuming these are independent, then p(a or b) is equal to p(a) + p(b). based on this, the answers to your questions are: servicability rating calculation probability difficult or very difficult .11 + .16 .27 difficult or average or easy .16 + .35 + .28 .79 average or better .35 + .28 + .10 .73 average or better presumes average or easy or very easy.
 Signed-numbers/565350: I need to use the distributive property to show this: -3x(x-3) This is what I got... -3x*x - -3x*3 Am I doing this right? The two negative signs don't look right.?. 1 solutions Answer 365766 by Theo(3504)   on 2012-01-31 03:17:33 (Show Source): You can put this solution on YOUR website!the problem is: -3x * (x-3) you distribute as follows: (-3x * x) + (-3x * -3) you then simplify this to: (-3x^2) + (9x) which becomes: -3x^2 + 9x your answer is: -3x*x - -3x*3 this simplifies to: -3x^2 + 9x looks good to me.
 Numbers_Word_Problems/564735: If the product of two numbers is zero, what can happen?1 solutions Answer 365500 by Theo(3504)   on 2012-01-30 09:34:24 (Show Source): You can put this solution on YOUR website!let a be one of the numbers. let b be the other of the numbers. your equation is a * b is equal to 0. assume a is equal to 0 and be is equal to any other number except 0. your equation becomes 0 * b = 0 assume b is equal to 0 and a is equal to any other number except 0. your equation becomes a * 0 = 0 assume both a and b are equal to 0. your equation becomes 0 * 0 = 0 your product will be equal to zero in all cases. at least one of the numbers has to be equal to 0. both can also be equal to 0. the value of the number that is not equal to 0 can be anything because anything * 0 will always equal 0.
 test/564770: 9yrs old wanting help with one maths problem. How to I write the value of 7 in 76,2221 solutions Answer 365473 by Theo(3504)   on 2012-01-30 06:20:17 (Show Source): You can put this solution on YOUR website!76,222 is equivalent to: 70,000 plus 6,000 plus 200 plus 20 plus 2.
 Permutations/564771: How many 6-digit numbers are there in 4,6,2,3,7 and 9 if repetition is not allowed?1 solutions Answer 365472 by Theo(3504)   on 2012-01-30 06:18:15 (Show Source): You can put this solution on YOUR website!there would be 6! = 6*5*4*3*2*1 = 720 if only 2 numbers (4 and 6), then the number of 2 digit numbers would be equal to 2! = 2 * 1 = 2 and the numbers would be 46, 64. if only 3 numbers (4 and 6 2), then the number of 3 digit numbers would be equal to 3! = 3 * 2 * 1 = 6 and the numbers would be 462, 426, 642, 624, 246, 264. 720 numbers with 6 digits is much harder to show, but you can see that the formula applies to any number of digits.
 Functions/564767: Suppose that y varies directly as x and inversely as z^2. If x and z are both decreased by 20%, then y? This is all I've got y=kx/z^2 ...I don't even know whether it's right.1 solutions Answer 365471 by Theo(3504)   on 2012-01-30 06:00:25 (Show Source): You can put this solution on YOUR website!you problem states that y varies directly as x and inversely as z^2. the formula for that would be: y = kx/z^2 you got started right because this agrees with what you showed. if x and y are each reduced by 20%, then you get: x - .2x = .8x z - .2z = .8z you would replace x with .8x and you would replace z with .8z to get: y = k(.8x)/(.8z)^2 you would simplify this to: y = .8kx / .64z^2 which you can further simplify to: y = 1.25kx/z^2 let's see how this would pan out. assume x = 64 and assume z = 8 and assume k = 1. that makes the math simple. your original equation of: y = kx/z^2 becomes: y = 1*64/8^2 which becomes: y = 64/64 which becomes: y = 1. now assume that x and y are both decreased by 20%. your equation of y = kx/z^2 becomes y = 1*(.8x) / (.8z)^2 which becomes: y = .8*64 / (.8*8)^2 which becomes: y = 51.2 / 6.4^2 which becomes: y = 51.2 / 20.96 which becomes: y = 1.25 we said that your equation became: y = 1.25kx/z^2 since your original x = 64 and your original y = 8, this equation becomes: y = 1.25(64)/(8^2) which becomes: y = 80/64 which becomes: y = 1.25 the answer comes out the same so the equation is good. your answer is: y = 1.25kx/z^2 a good reference on this type of problem can be found here: http://regentsprep.org/Regents/math/algtrig/ATE7/indexATE7.htm
 Square-cubic-other-roots/564746: 7×t√=3601 solutions Answer 365470 by Theo(3504)   on 2012-01-30 05:36:54 (Show Source): You can put this solution on YOUR website!i'm not exactly sure what you're asking. you may be asking: 7 * sqrt(t) = 360 in that case, you would divide both sides of that equation by 7 to get: sqrt(t) = 360/7 you would then square both sides of this equation to get: t = (360/7)^2 which is equivalent to: t = 360^2 / 7^2 which would be equivalent to: t = 129600 / 49. that can't be simplified further so that's your anser. in decimal form, that answer would be: t = 2644.897959 if that's not what you were looking for, then send me an email with what you were really looking for in english., something like: 7 times the square root of (t) = 360 would be an english equivalent of what i thought the problem was.
 Rectangles/564756: The camera has 10.1 million pixels. The product of the pixels across the screen times the pixels up the screen gives the number of pixels the camera has. The ratio of pixels across the screen to pixels up the screen is 4 : 3. How many pixels does this camera have across the screen? Explain what you are calculating as you solve the problem.1 solutions Answer 365469 by Theo(3504)   on 2012-01-30 05:26:39 (Show Source): You can put this solution on YOUR website!the ratio of horizontal pixels to vertical pixels is 4:3. let x = the number of horizontal pixels. let y = the number of vertical pixels. the ratio of x to y is 4 to 3 which can be shown as: x/y = 4/3 cross multiply to get: 3x = 4y solve for y to get: y = 3x/4 the total number of pixels is 10.1 million. since the total number of pixels is the number of horizontal pixels times the number of vertical pixels, then your equation would be: x * y = 10.1 since y = 3x/4, you can substitute for y in this equation to get: x * 3x/4 = 10.1 simplify this equation to get: 3x^2/4 = 10.1 multiply both sides of this equation by 4 to get: 3x^2 = 40.4 divide both sides of this equation by 3 to get: x^2 = 13.46666667 take the square root of both sides of this equation to get: x = 3.669695719 since x * y = 10.1, substitute for x in this equation to get: 3.669695719 * y = 10.1 divide both sides of this equation by 3.669695719 to get: y = 2.752271789 this suggest that: the number of horizontal pixels across the screen is 3.669695719 million. the number of vertical pixels across the screen is 2.752271789. since the ratio of horizontal pixels to vertical pixels is 4/3, then that ratio should also be equal to 3.669695719 / 2.752271789. your equation to see if that's true would be: 4/3 = 3.669695719 / 2.752271789. you would cross multiply to get: 4 * 2.752271789 = 3 * 3.669695719 you would simplify that to get: 11.00908716 = 11.00908716 which suggest that the ratios are the same which means you probably have the right numbers of horizontal pixels and vertical pixels. you would test that out by multiplying them together to get: 3.669695719 * 2.752271789 = 10.1. all the numbers check out so that's your answer.
 Probability-and-statistics/564751: For the following scores, what is Σ(X + 1)? Scores: A.2, b.0, c.4, d.2 I dont understand what Σ represents? I do understand that you do it lastly . So would you start out as... but then where do I go from here? A. Σ(2 + 1) B. Σ(0 + 1) C. Σ(4 + 1) D. Σ(2 + 1) thanks soo much for your help! 1 solutions Answer 365468 by Theo(3504)   on 2012-01-30 04:55:31 (Show Source): You can put this solution on YOUR website! Σ means "the sum of". example: the sum of (2 + 1) = 3 the sum of (0 + 1) = 1 the sum of (4 + 5) = 5 the sum of (2 + 1) = 3 usually that symbol is used to get the sum of a bunch of numbers in a list or table as shown below: i value 1 2 2 0 3 4 4 2 i is the name of the subscript that identifies the position of each element in the list or table. x is the name of the variable used for each element. each value in the table is identified by the variable name followed by the subscript. you would then identify each unique value in the table by the variable name followed by the subscript. in this table, that would be shown as: x[1] = 2 x[2] = 0 x[3] = 4 x[4] = 2 if you want to find the total value in the table, you would then be asked to provide the sum of x[i] for i = 1 to 4. this would be shown as Σ (x[i]) for i = 1 to 4 when i = 1, x[i] = 2 when i = 2, x[i] = 0 when i = 3, x[i] = 4 when i = 4, x[i] = 2 the Σ (x[i]) for i = 1 to 4 would then be equal to 2 + 0 + 4 + 2 = 8. judging by the way the question is posed, i suspect that all they want to know is the sum of (x + 1) when x is equal to the value shown. your answer would, in that case, be: A. Σ(2 + 1) = 3 B. Σ(0 + 1) = 1 C. Σ(4 + 1) = 5 D. Σ(2 + 1) = 3
 Geometry_Word_Problems/563898: 1 solutions Answer 365137 by Theo(3504)   on 2012-01-28 09:46:02 (Show Source): You can put this solution on YOUR website!if you are looking for the shortest distance between each of these, then i believe the table should look like this: E NNE NE SE WNW N 90 22.5 45 135 67.5 ENE 22.5 45 22.5 67.5 135 NW 135 67.5 90 180 22.5 WSW 157.5 135 157.5 112.5 45 SSW 112.5 180 157.5 67.5 90 in some cases you had the right distance, but it was the longer distance between them rather than the shorter distance. the shorter distance always had to be less than 180. i based my number on the following diagram: each interval is equal to 22.5 degrees. to calculate the distance between selected points, just count the number of dots for the shortest distance between them to come up with the difference. example: WSW to ESE is 6 dots 6 * 22.5 = 135 degrees. WSW is at 247.5 degrees ESE is at 112.5 degrees 247,5 - 112.5 = 135 degrees. another example: NNW to NNE is 2 dots 2 * 12.5 = 45 degrees 337.5 - 22.5 = 315 degrees this is actually the long way around because it is greater than 180 degrees. to convert it to the shortest way around, subtract it from 360 degrees to get 45 degrees. i saw only one distance where you actually calculated it wrong. i believe that was SSW to SE. you showed 247.5 and i calculated 67.5 the short way there and 292.5 the long way. anyway, that's my view of it. you can use the chart to double check your work as well.
 Miscellaneous_Word_Problems/563863: If x units of a product cost C dollars to manufacture and earn revenue of R dollars, the value of x where the expressions for C and R are equal are called the break-even quantity, the number of units that produce zero profit. Find the break-even quantity when C=15x+54000 and R=18x. Thank you!1 solutions Answer 365131 by Theo(3504)   on 2012-01-28 08:41:59 (Show Source): You can put this solution on YOUR website!C = 15x + 54000 R = 18x break even is when R = C this means that: 18x = 15x + 54000 subtract 15x from both sides of this equation to get: 3x = 54000 divide both sides of this equation by 3 to get: x = 18000 the breakeven point is when x = 18000 R = 18x = 18 * 18000 = 324000 C = 15x + 54000 = 15 * 18000 + 54000 = 270000b + 54000 = 324000