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 Mixture_Word_Problems/729873: Hi I am trying to do some word problems by using a system of equations, for example using x and y that way when I set up the two equations I can use either the subsitution method or elimination method. Here are my word problems hope you can help. (: 1. A total of \$12,000 is invested, part at 6% simmple interest and part at 3%. If the annual return from the two investments is the same, how much is invested at each rate? 2. A car travels 225 kilometers in the same time that a truck travels 195 kilometers. If the speed of the car is 10 kilometers per hour faster than the speed of the truck, find the speed of each vehicle. 1 solutions Answer 446337 by ankor@dixie-net.com(15657)   on 2013-03-24 16:44:57 (Show Source): You can put this solution on YOUR website!1. A total of \$12,000 is invested, part at 6% simple interest and part at 3%. If the annual return from the two investments is the same, how much is invested at each rate? let x = amt invested at 6% let y = amt invested at 3% Two equations x + y = 12000 and .06x = .03y divide both sides by .03, results 2x = y replace y with 2x in the 1st equation x + 2x = 12000 3x = 12000 x = 12000/3 x = 4000 I'll let you find y, check the solutions in the interest equation : : 2. A car travels 225 kilometers in the same time that a truck travels 195 kilometers. let x = car speed, let y = truck speed write a time equation; time = dist/speed = Cross multiply 225y = 195x divide both sides by 5, results: 45y = 39x : " If the speed of the car is 10 kilometers per hour faster than the speed of the truck," x - y = 10 x = y + 10 "find the speed of each vehicle." replace x with (y+10) in the 1st simplified equation 45y = 39(y+10) 45y = 39y + 390 45y - 39y = 390 6y = 390 y = 390/6 y = 65 mph, the speed of the truck I'll let you find the speed of the car, check your solutions in both equations
 Quadratic_Equations/729978: Hello, I need help solving this equation please. It is supposed to be written in quadratic form, but I do not know how to write it out either. 1 solutions Answer 446320 by ankor@dixie-net.com(15657)   on 2013-03-24 16:16:31 (Show Source): You can put this solution on YOUR website! Factor out a^3 Factor again a^3(a+5)(a+1) = 0 three solutions a = 0 a = -5 a = -1
 Polynomials-and-rational-expressions/729944: Find the zeros of each function by factoring and using the zero product property 3x^3 - 36x^2 + 108x1 solutions Answer 446311 by ankor@dixie-net.com(15657)   on 2013-03-24 15:59:58 (Show Source): You can put this solution on YOUR website!Find the zeros of each function by factoring and using the zero product property 3x^3 - 36x^2 + 108x = 0 factor out 3x 3x(x^2 - 12x + 36) = 0 factor again 3x(x-6)(x-6) = 0 two solutions x = 0 and x = 6
 Quadratic_Equations/729636: let k be an integer and p is a prime such that the quadratic equation x^2+kx+p=0 has two distinct positive integer solutions. The value of (k+p)=,,?1 solutions Answer 446220 by ankor@dixie-net.com(15657)   on 2013-03-23 21:38:59 (Show Source): You can put this solution on YOUR website!let k be an integer and p is a prime such that the quadratic equation x^2 + kx + p = 0 has two distinct positive integer solutions. The value of (k+p)=,,? : If p is prime and it has two integer solutions, one of the solutions has to be 1 therefore k = p + 1 x^2 + (p+1)x + p = 0 " The value of (k+p)=" (p+1) + p = 2p+1
 Rate-of-work-word-problems/729747: A,B,and C undertook a construction project. A and B worked together the first 6 days and finished 1/3 of the project, then B and C worked together for 2 days on 1/4 of the remaining. And the rest of the project was completed by A,B, and C working together for 5 days. They were paid \$1800 in total. If each were to be paid fairly, according to how much work he contributed, how much should B receive?1 solutions Answer 446215 by ankor@dixie-net.com(15657)   on 2013-03-23 21:18:41 (Show Source): You can put this solution on YOUR website!A,B,and C undertook a construction project. Let the completed project = 1800 then A and B worked together the first 6 days and finished 1/3 of the project, Their work is equal to 1/3 of 1800 or 600 Assuming they work at the same rate A = 300 B = 300 : then B and C worked together for 2 days on 1/4 of the remaining. 1/4 of the remaining (1200) = 300 B = 150 C = 150 : And the rest of the project was completed by A,B, and C working together for 5 days. The amt they did: 1800 - 600 - 300 = 900 A = 300 B = 300 C = 300 They were paid \$1800 in total. If each were to be paid fairly, according to how much work he contributed, how much should B receive? B = 300 + 150 + 300 = \$750 is B's share
 Equations/729754: A two digit number and the resulting number when the digits are reversed are in the ratio 2:9.If the sum of the digits is 9,Find the original number.1 solutions Answer 446208 by ankor@dixie-net.com(15657)   on 2013-03-23 20:57:52 (Show Source): You can put this solution on YOUR website!let a = the 10's digit of the original number let b = the units : "A two digit number and the resulting number when the digits are reversed are in the ratio 2:9." = Cross multiply 9(10a+b) = 2(10b+a) 90a + 9b = 20b + 2a 90a - 2a = 20b - 9b 88a = 11b Simplify divide by 11 8a = b : "If the sum of the digits is 9, a + b = 9 replace b with 8a a + 8a = 9 9a = 9 a = 1 then b = 8 : 18 is the original number : : : Check this =
 Miscellaneous_Word_Problems/729756: How do i figure out the proportion 168 to 300? ive got an answer from someone but dont know how to figure it out, my answers are 168 to 300 is as 84 to 150 is as 42 to 72 is as 21 to 25... but how do you get to the anwer (show my work)?1 solutions Answer 446207 by ankor@dixie-net.com(15657)   on 2013-03-23 20:50:22 (Show Source): You can put this solution on YOUR website!Just write it as fraction: Reduce the fraction, which is apparently you tried to do Divide the numerator and denominator by 4 getting which is 42:75
 Age_Word_Problems/729596: Juan is "g" years old and Eva is 2 years younger than Juan. Find the sum of their ages in g years time, in terms of g. 1 solutions Answer 446204 by ankor@dixie-net.com(15657)   on 2013-03-23 20:42:30 (Show Source): You can put this solution on YOUR website!: Juan is "g" years old g = J's age and Eva is 2 years younger than Juan. (g-2) = E's age : Find the sum of their ages in g years time, in terms of g. S(g) = (g+g) + (g-2+g) S(g) = 4g - 2
 logarithm/729680: Solve. Log base 8 of 2x + log base 8 of 5 = 11 solutions Answer 446191 by ankor@dixie-net.com(15657)   on 2013-03-23 19:00:09 (Show Source): You can put this solution on YOUR website! Solve. Log base 8 of 2x + log base 8 of 5 = 1 = 1 addition of logs is multiply = 1 = 1 The exponent equiv = 10x or 10x = 8 x = 8/10 x = .8
 Rate-of-work-word-problems/729260: Working together, 4 skilled workers can complete a job in 5 days. However, 5 semi-skilled workers can complete the same job in 6 days. If 1 semi-skilled and 2 skilled workers work together, how long does it take for them to complete the same job?1 solutions Answer 446179 by ankor@dixie-net.com(15657)   on 2013-03-23 16:52:05 (Show Source): You can put this solution on YOUR website!Working together, 4 skilled workers can complete a job in 5 days. therefore: 4 * 5 = 20 man-days for skilled men complete the job : However, 5 semi-skilled workers can complete the same job in 6 days. therefore: 5 * 6 = 30 man-days for semi-skilled men to complete the job : If 1 semi-skilled and 2 skilled workers work together, how long does it take for them to complete the same job? Let d = number of days for them to complete the job. Let the completed job = 1, Each group will do a fraction of the job, the two fractions add up to 1 : + = 1 multiply by 60, resulting in: 3(2d) + 2(1d) = 60 6d + 2d = 60 8d = 60 d = 60/8 d = 7.5 days for them to complete the job together
 test/728865: a train, an hour after starting, meets with an accident which detains it an hour .after which it proceed at 3/5 of its former rate arrives 3hrs after time but had the accident happened 50miles farther on the line, it would have arrived 1.5hr sooner.find the length of the journey1 solutions Answer 446156 by ankor@dixie-net.com(15657)   on 2013-03-23 13:47:42 (Show Source): You can put this solution on YOUR website!A train, an hour after starting, meets with an accident which detains it an hour. After which it proceed at 3/5 of its former rate, arriving 3 hrs late. But had the accident happened 50miles farther on the line, it would have arrived 1.5hr sooner. Find the length of the journey : let s = normal speed of the train (s also = the dist traveled the 1st hr) then .6s = speed after the accident : let d = distance of the journey and d/s = normal time of the journey : Write a time equation for the 1st scenario : normal speed time + stopped time + 3/5 speed time - normal time = 3 hrs 1 + 1 + () - = 3 2 + () - = 3 multiply by .6s, resulting in: 2(.6s) + d - s - .6d = .6s(3) 1.2s + d - s - .6d = 1.8s combine like terms d - .6d = 1.8s - 1.2s + s .4d = 1.6s divide both sides by .4 d = s d = 4s : An equation for the 2nd scenario " but had the accident happened 50miles farther on the line, it would have arrived 1.5hr sooner." 2 + + () - = 3 - 1.5 2 + + () - = 1.5 Multiply by .6s .6s(2) + .6(50) + d - s - 50 - .6d = .6s(1.5) 1.2s + 30 + d - s - 50 - .6d = .9s Combine like terms 1.2s - s - .9s + d -.6d -50 + 30 = 0 -.7s + .4d - 20 = 0 -.7s + .4d = 20 Replace d with 4s -.7s + .4(4s) = 20 -.7s + 1.6s = 20 .9s = 20 s = 20/.9 s = 22.2 mph then 4(22.2) = 88.8 mi is the journey
 Volume/729402: A plastic container is in the shape of a rectangular prism. Its base has an area of 30 square inches. Its height is 7 inches. The plastic container is filled to the top with water and emptied into a fish tank. The fish tank has a base that is 20 inches by 8 inches, and it has a height of 14 inches. How high will the water reach up the side of the fish tank?1 solutions Answer 445966 by ankor@dixie-net.com(15657)   on 2013-03-22 19:43:49 (Show Source): You can put this solution on YOUR website! A plastic container is in the shape of a rectangular prism. Its base has an area of 30 square inches. Its height is 7 inches. The plastic container is filled to the top with water and emptied into a fish tank. The fish tank has a base that is 20 inches by 8 inches, and it has a height of 14 inches. How high will the water reach up the side of the fish tank? : Find the volume of the water in the plastic container: V = 30 * 7 V = 210 cu/inches : Find the height (h) of the water in the tank 20 * 8 * h = 210 160h = 210 h = 210/160 h = 1.3125 inches
 Quadratic_Equations/729502: I have a question about quadratic equation. I know if you need to square a negative number then it will be that number with an I at the end but we haven't learned that yet so I'm not sure if I'm doing the problem right. Here's what I'm doing: 4x^2-6x+2=0 6 plus or minus square root of (-6^2-4(4)(2)over 2(4) 6 plus or minus square root of (-36-72) over 8 6 plus of minus square root of (-108) over 8 Can you tell me what I am doing wrong? Or would the problem be considered non solvable? 1 solutions Answer 445905 by ankor@dixie-net.com(15657)   on 2013-03-22 17:53:38 (Show Source): You can put this solution on YOUR website!4x^2-6x+2=0 This equation can be factored Factor out 2 first 2(2x^2 - 3x + 1) = 0 Factor what's left (2x - 1)(x - 1) = 0 Two solutions 2x = 1 x = 1/2 and x = 1
 Travel_Word_Problems/729392: If a slow engine leaves the tracks 1 1/2 hours earlier than a faster train that travels 1 1/2 times faster than the slow train, how long will it take for the fast train to catch up to the slow train??1 solutions Answer 445834 by ankor@dixie-net.com(15657)   on 2013-03-22 09:46:52 (Show Source): You can put this solution on YOUR website!If a slow engine leaves the tracks 1 1/2 hours earlier than a faster train that travels 1 1/2 times faster than the slow train, how long will it take for the fast train to catch up to the slow train?? : let t = travel time of the fast train then (t+1.5) = the travel time of the slow train : let s = speed of the slow train then 1.5s = speed of the fast train : Write a distance equation, dist = speed * time, When the fast catches the slow, they will have traveled the same distance. 1.5st = s(t+1.5) 1.5st = st + 1.5s Divide thru by s 1.5t = t + 1.5 1.5t - t = 1.5 .5t = 1.5 mult by 2 t = 3 hrs for the fast to catch the slow : : Check this, let's assume the slow train speed is 40 mph, then the fast = 60 They should have traveled the same dist 40 * 4.5 = 180 mi 60 * 3 = 180 mi
 Expressions-with-variables/728392: I need help learning how to solve this word problem. I'm not sure how to start. A natural number is 4 more than another natural number. When the reciprocal of the greater number is subtracted from the reciprocal of the lesser number, the difference is . What are the two numbers? 1 solutions Answer 445422 by ankor@dixie-net.com(15657)   on 2013-03-20 10:02:39 (Show Source): You can put this solution on YOUR website!A natural number is 4 more than another natural number. When the reciprocal of the greater number is subtracted from the reciprocal of the lesser number, the difference is . What are the two numbers? : You did not give us the difference, so am going to give you a method : Let a and b = the two numbers, let a be the greater number : Write an equation for each statement: : "A natural number is 4 more than another natural number." a = b + 4 : " When the reciprocal of the greater number is subtracted from the reciprocal of the lesser number, the difference is ." - = ? multiply both sides by ab b - a = ?ab Add a to both sides b = ?ab + a factor out a b = a(?b + 1) Replace a with (b+4), from the 1st statement b = (b+4)(?b+1) FOIL this, develop a quadratic equation, find b : Let me know how you do with this. CK
 Expressions-with-variables/728391: Hello! I need help solving this...It takes Marcy’s apprentice 9 h longer to build a deck than it takes Marcy, an experienced carpenter. When they work together, they can build the deck in 20h. How long would it take each person to build the deck working alone? 1 solutions Answer 445416 by ankor@dixie-net.com(15657)   on 2013-03-20 09:45:11 (Show Source): You can put this solution on YOUR website!It takes Marcy’s apprentice 9 h longer to build a deck than it takes Marcy, an experienced carpenter. When they work together, they can build the deck in 20h. How long would it take each person to build the deck working alone? : let m = M's time to build the deck alone then (m+9) = Apprentice time to do the job : Let the completed job = 1 : Each will do a fraction of the job, the two fractions add up to 1. : A typical shared work equation : + = 1 multiply by m(m+9), cancel the denominators, resulting in: 20(m+9) + 20m = m(m+9) 20m + 180 + 20m = m^2 + 9m Combine like terms on the right side 0 = m^2 + 9m - 40m - 180 A quadratic equation m^2 - 31m - 180 = 0 You can use the quadratic formula here, but this will factor to (m-36)(m+5) = 0 The positive solution m = 36 hrs M, working alone then 36 + 9 = 45 hrs the apprentice working alone : : See if that adds up using a calc + = 1 .56 + .44 = 1
 Metalworking/728451: If totally 25 workers working for 7 hours a day completing a particular piece of work in 28 days,in howmany days 20 workers working for 6 hours a day wil complete same work?1 solutions Answer 445411 by ankor@dixie-net.com(15657)   on 2013-03-20 09:25:50 (Show Source): You can put this solution on YOUR website!If totally 25 workers working for 7 hours a day completing a particular piece of work in 28 days, in how many days 20 workers working for 6 hours a day will complete same work? : Find number of man-hours required to complete the job. 25*7*28 = 4900 man-hrs : let d = number of days required by 20 workers, working 6 hr/day 20*6*d = 4900 120d = 4900 d = 4900/120 d = 40.833 days which is: 40 days + .833(6) = 5 hrs : Check this 40*6*20 = 4800 man-hrs 20 * 5 = 100 man-hrs ---------------------- total 4900 man-hrs
 Travel_Word_Problems/727906: A plane covers 2,160 miles in 5.5 hours. What is the average speed of the plane 1 solutions Answer 445242 by ankor@dixie-net.com(15657)   on 2013-03-19 08:07:02 (Show Source): You can put this solution on YOUR website! A plane covers 2,160 miles in 5.5 hours. What is the average speed of the plane? : Remember speed = dist/time : s =
 Vectors/727448: i need help solving this problem :/ solve by using the addition method: 5x + 3y - z = 5 3x - 2y + 4z = 13 4x + 3Y + 5z = 221 solutions Answer 445142 by ankor@dixie-net.com(15657)   on 2013-03-18 17:23:33 (Show Source): You can put this solution on YOUR website!solve by using the addition method: 5x + 3y - z = 5 3x - 2y + 4z = 13 4x + 3Y + 5z = 22 : Multiply the 2nd equation by -1 5x + 3y - z = 5 -3x+ 2y - 4z = -13 4x + 3Y + 5z = 22 --------------------addition eliminates z 6x + 8y = 14 : multiply the 1st equation by 4, add to the 2nd equation 20x + 12y - 4z = 20 3x - 2y + 4z = 13 ------------------addition eliminates z 23x + 10y = 33 : multiply the 1st two unknowns by -5, multiply the 2nd by 4 -30x + -40y = -70 92x + 40y = 132 --------------------addition eliminates y, find x 62x = 62 x = 1 : Find y 6x + 8y = 14 6 + 8y = 14 8y = 14 - 6 8y = 8 y = 1 : Find z 3x - 2y + 4z = 13 3 - 2 + 4z = 13 4z = 13 - 1 4z = 12 z = 12/4 z = 3 : : Check the solutions in the 3rd equation 4x + 3Y + 5z = 22 4 + 3 + 5(3) = 22 7 + 15 = 22; confirms our solutions
 Travel_Word_Problems/727476: A plane is traveling at 600 miles per hour. How many feet per second is it traveling?1 solutions Answer 445114 by ankor@dixie-net.com(15657)   on 2013-03-18 14:39:16 (Show Source): You can put this solution on YOUR website! = 880 ft/sec
 logarithm/727450: Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this. 1n 2x=4 Possible answers: A) 109.196 B) 27.300 C) 54.598 D) 7.389 E) 27.2991 solutions Answer 445101 by ankor@dixie-net.com(15657)   on 2013-03-18 09:35:45 (Show Source): You can put this solution on YOUR website!Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this. 1n 2x=4 Write the exponent equiv. e^4 = 2x 2.7183^4 = 2x 54.598 = 2x x = x = 27.299