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 Numbers_Word_Problems/265078: What is, "The sum of two integers is thirty-eight. Nine times the smaller integer is 23 more than 2 times the larger integer. Find the integers." 1 solutions Answer 195166 by ankor@dixie-net.com(15623)   on 2010-02-04 08:48:01 (Show Source): You can put this solution on YOUR website!Let x & y be the two integers, (x is the smaller) : write an equation for each statement: : "The sum of two integers is thirty-eight. x + y = 38 y = (38-x), use this for substitution : "Nine times the smaller integer is 23 more than 2 times the larger integer." 9x = 2y + 23 : Find the integers replace y in the above equation with (38-x) 9x = 2(38-x) + 23 9x = 76 - 2x + 23 9x + 2x = 76 + 23 11x = 99 x = x = 9 : I'll let you find y, check solutions in the 2nd equation
 Functions/265079: Solve for p 1/p+1/q=1/f I came up with the lcm:fpq so now it turns into this: fq/fpq+fp/fpq=pq/fpq But I don't know where to go from there. I saw someone else just do this: fq+fp=pq but it seemed confusing because I don't know what they did with the denominator1 solutions Answer 195155 by ankor@dixie-net.com(15623)   on 2010-02-04 08:16:29 (Show Source): You can put this solution on YOUR website!Solve for p the common denominator is pqf, multiply each term by pqf, this gets rid of the denominators, results: qf + pf = pq : Subtract qf from both sides pf = pq - qf : subtract pq from both sides pf - pq = -qf : Factor out p on the right p(f-q) = -qf : Divide both sides by (f-q), results p = : Did this make sense to you now?
 Expressions-with-variables/265342: E= (Th-Tc) / Th solve for Th1 solutions Answer 195120 by ankor@dixie-net.com(15623)   on 2010-02-03 22:02:55 (Show Source): You can put this solution on YOUR website!E= (Th-Tc) / Th solve for Th : which is : Multiply both sides by Th Th(E-1) = -Tc : divide both sides by (E-1) Th =
 Expressions-with-variables/265329: Variables on both sides? Can someone expain to me how to solve this? I'm trying to help my daughter with her home work and am not familar with this. Probem: 7x-1=-5+3x Thanks1 solutions Answer 195116 by ankor@dixie-net.com(15623)   on 2010-02-03 21:51:01 (Show Source): You can put this solution on YOUR website!Problem: 7x - 1 = -5 + 3x : Perform the necessary operations (+,-,/*) on both sides of the equation to get the unknown (x) on one side by itself, usually on the left but doesn't have to be 7x - 1 = -5 + 3x Subtract 3x from both sides 7x - 3x - 1 = -5 + 3x - 3x : which is 4x - 1 = -5 + 0 ; or just 4x - 1 = -5 ; add 1 to both sides 4x - 1 + 1 = -5 + 1 4x + 0 = -4 ; or just 4x = -4 : Divide both sides by 4 x = 1x = -1 or just x = -1 : : Check solution by substituting for x in the original equation 7x - 1 = -5 + 3x 7(-1) - 1 = -5 + 3(-1) do the math -7 - 1 = -5 - 3 which is -8 = -8, equality confirms our solution of x = -1
 Age_Word_Problems/265299: If Sally adds four times her age four years from now to five times her age five years from now, she gets ten times her current age. how old will sally be five years from now?1 solutions Answer 195115 by ankor@dixie-net.com(15623)   on 2010-02-03 21:40:13 (Show Source): You can put this solution on YOUR website!If Sally adds four times her age four years from now to five times her age five years from now, she gets ten times her current age. 4(s+4) + 5(s+5) = 10s 4s + 16 + 5s + 25 = 10s 16 + 25 = 10s - 4s - 5s 41 = s : Sally is 41 now : how old will sally be five years from now? Sally will be 46
 Geometry_Word_Problems/265319: I just can't figure out how to solve this word problem. I get confused with fractions. An architect designs a rectangular flower garden such that the width is two-thirds of the length. If 260 feet of antigue picket fencing are to be used to enclose the garden, find the dimensions of the garden. I am so confused and would really appreciate help with this one!1 solutions Answer 195112 by ankor@dixie-net.com(15623)   on 2010-02-03 21:30:44 (Show Source): You can put this solution on YOUR website!An architect designs a rectangular flower garden such that the width is two-thirds of the length. If 260 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden. : This is a perimeter problem 2L + 2W = 260 : It says,"the width is two-thirds of the length.", therefore we can write: W = L : Substitute L for W in the perimeter equation 2L + 2(L) = 260 which is 2L + L = 260 Get rid of the denominator multiply both sides by 3, results 3(2L) + 4L = 3(260) 6L + 4L = 780 10L = 780 L = L = 78 ft is the length and (78) = 52 ft is the width : : Check solutions by finding the perimeter 2(78) + 2(52) = 156 + 104 = 260; confirms our solution
 Word_Problems_With_Coins/264990: I have a bag full of nickels weighing 30 pounds; how much is it worth in dollars?1 solutions Answer 195111 by ankor@dixie-net.com(15623)   on 2010-02-03 21:16:20 (Show Source): You can put this solution on YOUR website!I have a bag full of nickels weighing 30 pounds; how much is it worth in dollars? : According to the us mint, 1 nickel weigh 5 grams : 30 * .4536 = 13.608 kg which is 13,608 grams = 2721.6 ~ 2722 nickels in 30 lb 20 nickels in a dollar = \$136.10
 Graphs/265250: In this equation what is the SLOPE and what is the Y-INTERCEPT? 4y - 8x + 12 = 01 solutions Answer 195079 by ankor@dixie-net.com(15623)   on 2010-02-03 19:35:34 (Show Source): You can put this solution on YOUR website!4y - 8x + 12 = 0 : Put the equation into the slope/intercept form (y = mx + b) 4y = 8x - 12 : divide by 4 y = 2x - 3 : slope is 2, y intercept is -3
 Numbers_Word_Problems/264965: Four times the difference of a number and one is equal to six times the sum of the number and three. Find the number.?1 solutions Answer 195076 by ankor@dixie-net.com(15623)   on 2010-02-03 19:30:13 (Show Source): You can put this solution on YOUR website!Four times the difference of a number and one is equal to six times the sum of the number and three. 4(x-1) = 6(x + 3) : Find the number.? Can you do it now? (the solution is negative)
 Equations/264935: If Dixi has x amount of ice-creams, Cena has 10 more than Dixi, Malida has half as many as Dixi, together they have a total of 50 ice-creams. How many ice-creams does Dixi have?1 solutions Answer 195073 by ankor@dixie-net.com(15623)   on 2010-02-03 19:24:41 (Show Source): You can put this solution on YOUR website!If Dixi has x amount of ice-creams, Cena has 10 more than Dixi, c = x + 10 : Malida has half as many as Dixi, m = .5x : together they have a total of 50 ice-creams. x + (x+10) + .5x = 50 2.5x = 50 - 10 x = x = 16 ice creams for Dixi : Check: 16 + 26 + 8 = 50
 Numbers_Word_Problems/265029: The product of two whole numbers is 36. When the first number is added to three times the second number, the answer is 31. what are the numbers?1 solutions Answer 195069 by ankor@dixie-net.com(15623)   on 2010-02-03 19:17:01 (Show Source): You can put this solution on YOUR website!The product of two whole numbers is 36. x * y = 36 x = : When the first number is added to three times the second number, the answer is 31. x + 3y = 31 ; Replace x with + 3y = 31 : multiply by y, results 36 + 3y^2 = 31y ; A quadratic equation 3y^2 - 31y + 36 = 0 ; Factors to (3y - 4)(y - 9) = 0 : two solutions y = 9, then x = 4 and 3y = 4, y = ; then x = 27
 Miscellaneous_Word_Problems/265136: I have trouble with word problems,I don't know where to begin. The problem is Plastics Unlimited plans to produce a one component vertical file by bending the long side of an 8-in. by 14-in. sheet of plastic along two lines to form a U shape. A. Express the volume of the file as a function of the height x, in inches, of the file. B. Find the domain of the function. Thank You for your help.1 solutions Answer 195057 by ankor@dixie-net.com(15623)   on 2010-02-03 19:01:30 (Show Source): You can put this solution on YOUR website! produce a one component vertical file by bending the long side of an 8-in. by 14-in. sheet of plastic along two lines to form a U shape. : A. Express the volume of the file as a function of the height x, in inches, of the file. Height is given as x, therefore the width = (14-2x): x|__|x is the shape Vol = x*(14-2x)*8 V = (-2x^2 + 14x) * 8 V = -16x^2 + 112x : B. Find the domain of the function. Looking at the expression (14-2x), the domain has to be >0 and <7
 Linear_Equations_And_Systems_Word_Problems/265216: Cara like candles. She also like mathematic and was thinking about using algebra to answer a question that she had about two of her candles. Her taller candle is 16 centimeters tall. each hour which it burns makes the candle lose 2.5 centimeter in height for each hour that it burns. Cara need your help to determine whether these two candles would ever reach the same height at the same time if allowed to burn the same length of time. She wants to know what height the two candles would be at that time. If it is not possible, she want to know why. explain, use multiple representations, and justify your results.1 solutions Answer 195049 by ankor@dixie-net.com(15623)   on 2010-02-03 18:48:49 (Show Source): You can put this solution on YOUR website!We need to know the height and burn rate of the 2nd candle : Editing the problem with some additional information from your comment: : : taller candle is 16 centimeters tall. each hour which it burns makes the candle lose 2.5 centimeter in height for each hour that it burns. : THe height of the 2nd candle in 12 centimeters, and the burn rate is 1.5 centimeters for each hour it burns. : determine whether these two candles would ever reach the same height at the same time if allowed to burn the same length of time. She wants to know what height the two candles would be at that time. ; Let t = time when they are the same height (hrs) : 16 - 2.5t = 12 - 1.5t 16 - 12 = -1.5t + 2.5t 4 = t; this will occur in 4 hrs : Finding the height of each candle after 4 hrs will prove this is true : Substituting 4 for t in each equation the 16cm candle 16 - 2.5t = 16 - 4(2.5) = 16 - 10 = 6 cm and for the 12cm candle 12 - 1.5t = 12 - 4(1.5) = 12 - 6 = 6 cm; That's the height of the two candles and we proved it. :
 Numbers_Word_Problems/264997: Two numbers are in the ratio 3:7. Two fifths of their sum is 32. Find the numbers. 1 solutions Answer 194995 by ankor@dixie-net.com(15623)   on 2010-02-03 16:37:08 (Show Source): You can put this solution on YOUR website!Two numbers are in the ratio 3:7. Two fifths of their sum is 32. Find the numbers. : Let x = the multiplier then 3x = one number and 7x = the other number : "Two fifths of their sum is 32." (3x + 7x) = 32 : (10x) = 32 : 4x = 32 x = x = 8 is the multiplier : 3(8) = 24 is one number 7(8) = 56 is the other number ; : Is this true? (24 + 56) = (80) = 32, it is.
 Travel_Word_Problems/264958: Fifteen minutes after a boy left for school on his bike, his mother noticed that he left his term paper on the kitchen table. His mother left home, driving at a rate of 32 mph, to catch up to him. If he had been bicycling at a rate of 8 mph, how long did it take his mother to catch up with him?1 solutions Answer 194991 by ankor@dixie-net.com(15623)   on 2010-02-03 16:28:00 (Show Source): You can put this solution on YOUR website!Fifteen minutes after a boy left for school on his bike, his mother noticed that he left his term paper on the kitchen table. His mother left home, driving at a rate of 32 mph, to catch up to him. If he had been bicycling at a rate of 8 mph, how long did it take his mother to catch up with him? : Change 15 min to .25 hrs : Let t = travel time of the mother then (t+.25) = travel time of the boy : When Mom catches boy they will have traveled the same distance, write a distance equation Dist = speed * time : Mom's dist = boy's dist 32t = 8(t+.25) 32t = 8t + 2 32t - 8t = 2 24t = 2 t = * 60 = 5 minutes to catch him : : Check solution by finding the dist each traveled (boy's travel time 15 + 5 = 20 min) 5/60(32) = 2.67 mi 20/60(8) = 2.67 mi
 Equations/265091: I strongly attempted to do this problem on my homework it's one of the one's I can't solve I'll greatly appreciate if you can help me with it, please explain it if you can here's the problem. -9w+17=7-4w1 solutions Answer 194977 by ankor@dixie-net.com(15623)   on 2010-02-03 14:58:13 (Show Source): You can put this solution on YOUR website!-9w + 17 = 7 - 4w we want to get unknown on the left and the numerical values on the right Add 4w to both sides, results -9w + 4w + 17 = 7 : Subtract 17 from both sides, results: -9w + 4w = 7 - 17 ; combine like terms -5w = -10 ; The variable always has to be positive, multiply both sides by -1 5w = +10 divide both sides by 5 w = w = 2 : : Check solution in original equation, check for equality -9w + 17 = 7 - 4w -9(2) + 17 = 7 - 4(2) -18 + 17 = 7 - 8 -1 = -1; confirms our solution
 Linear-equations/265006: At 11am, billy and leon set off towards each other from different places 32km apart. billy cycled at 20 km per hour and leon walked at 5km per hour. draw distance time graphs of their journeys on the same grid to find out: 1. the time at which they met 2. the time at which they are 12km apart.1 solutions Answer 194976 by ankor@dixie-net.com(15623)   on 2010-02-03 14:49:24 (Show Source): You can put this solution on YOUR website!At 11am, billy and leon set off towards each other from different places 32km apart. billy cycled at 20 km per hour and leon walked at 5km per hour. draw distance time graphs of their journeys on the same grid to find out: : referenced to Billy's starting point d = distance from the reference point t = time (hrs) Two equations d = 20t; (Billy, Red) d = 32 - 5t; (Leon, Green) Graphing the two equations. Time on the x axis, distance from Ref on y axis 1. the time at which they met We can estimate using the graph, but we calculate it exactly (equal dist from ref) 20t = 32 - 5t 20t + 5t = 32 25t = 32 t = t = 1.28 hrs or 1 hr + .28(60) ~ 17 minutes 11 am + 1:17 = 12:17 pm : 2. the time at which they are 12km apart. Subtract Billy's equation from Leon's equation, find t (32-5t) - 20t = 12 -25t = 12 - 32 -25t = -20 t = t = .8 hrs, .8(60) = 48 min which would be 11:48 am
 Rate-of-work-word-problems/264833: please help Patrice,by himself, can paint four rooms in 10 hours. if he hire April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her to paint four rooms?1 solutions Answer 194950 by ankor@dixie-net.com(15623)   on 2010-02-03 11:32:16 (Show Source): You can put this solution on YOUR website!Patrice,by himself, can paint four rooms in 10 hours. if he hire April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her to paint four rooms? : Let x = time when A work's alone Let the completed job = 1 (the painting of 4 rooms) : A typical shared work equation Each will do a fraction of the work, the two fractions add up to 1 + = 1 Multiply by 10x, the results: 6x + 10(6) = 10x 6x + 60 = 10x 60 = 10x - 6x 60 = 4x x = x = 15 hrs for A to do the job alone ; : Check solution on a calc, enter 6/10 + 6/15 = 1
 Percentage-and-ratio-word-problems/264826: How much water must be evaporated from 32 ounces of a 4% salt solution to make a 6% salt solution?1 solutions Answer 194946 by ankor@dixie-net.com(15623)   on 2010-02-03 11:12:13 (Show Source): You can put this solution on YOUR website!How much water must be evaporated from 32 ounces of a 4% salt solution to make a 6% salt solution? : Let x = amt of water required to be evaporated ; Really a simple equation .04(32) = .06(32-x) 1.28 = 1.92 - .06x +.06x = 1.92 - 1.28 .06x = .64 x = x = 10 oz to be evaporated : : Check solution .04(32) = .06(32-10.67) 1.28 = .06(21.33) 1.28 = 1.28, note the amt of salt stays the same, only the amt of water changes
 Linear_Algebra/264813: s=pie(r+R) solve for r1 solutions Answer 194942 by ankor@dixie-net.com(15623)   on 2010-02-03 10:26:55 (Show Source): You can put this solution on YOUR website!s=pie(r+R) solve for r : s = : = s : multiply what's inside the brackets = s : = : r =
 Linear_Equations_And_Systems_Word_Problems/264213: A choir is singing in a festival. On the first night 12 people were absent so they stood in 5 equal rows. On the second night only 1 was absent so they stood in 6 equal rows. The same number of people stood in each row each night. How many people are in the choir? 5-12x 6-1x1 solutions Answer 194863 by ankor@dixie-net.com(15623)   on 2010-02-02 21:52:01 (Show Source): You can put this solution on YOUR website! A choir is singing in a festival. On the first night 12 people were absent so they stood in 5 equal rows. On the second night only 1 was absent so they stood in 6 equal rows. The same number of people stood in each row each night. How many people are in the choir? : Let x = no. of people in the choir Let r = no. of people in each row (same both nights) : x - 1 = 6r; 2nd night x -12 = 5r; 1st night -------------------------subtraction eliminates x, find r 0 + 11 = r 11 people in each row both nights : Find x x - 12 = 5(11) x = 55 + 12 x = 67 people in the choir ; Check solution in the 2nd night equation 67 - 1 = 6*11
 Word_Problems_With_Coins/264677: Eight years ago, Melanie was half the age she will be in 3 years. How old is she now?1 solutions Answer 194862 by ankor@dixie-net.com(15623)   on 2010-02-02 21:38:03 (Show Source): You can put this solution on YOUR website!let m = her ages now : write an equation for what it says: : "Eight years ago, Melanie was half the age she will be in 3 years." m - 8 = .5(m + 3) m - 8 = .5m + 1.5 m - .5m = 1.5 + 8 .5m = 9.5 m = m = 19 yrs : : Check that in the given statement; 19 - 8 = .5(19+3) 11 = .5(22)
 Expressions-with-variables/264696: Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 mph and train B is traveling at 70 mph. Train A passes a station at 6:25 a.m. If train B passes the same station at 6:55 a.m. at what time will train B catch up to train A? UGH! I can not even set up an equation for this one! Will someone PLEASE HELP?!!1 solutions Answer 194860 by ankor@dixie-net.com(15623)   on 2010-02-02 21:32:02 (Show Source): You can put this solution on YOUR website!Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 mph and train B is traveling at 70 mph. Train A passes a station at 6:25 a.m. If train B passes the same station at 6:55 a.m. at what time will train B catch up to train A? : from the given information, we know that train B is 30 min (1/2 hr) behind train A, when train A passes the station : The distance between the trains at this time: * 70 = 35 mi : Let t = time required for train B to catch train A : write a distance equation: Dist = speed * time : Train B travel dist = Train A travel dist + 35 mi 70t = 60t + 35 70t - 60t = 35 10t = 35 t = t = 3.5 hr or 3 hrs 30 min : Find the time: 6:25 + 3:30 = 09:55 am, B catches A : : Check this by finding the distance each train traveled in 3.5 hr. 3.5*60 = 210 mi 3.5*70 = 245 mi, 35 mi further
 Geometry_Word_Problems/264173: Volume of a can of coke If a can of coke contains 12 fluid ounces and the diameter of the can is 2.375 in., then what is the height of the can?(one fluid ounce equals approximately 1.8in.3rd.)1 solutions Answer 194855 by ankor@dixie-net.com(15623)   on 2010-02-02 21:09:34 (Show Source): You can put this solution on YOUR website!If a can of coke contains 12 fluid ounces and the diameter of the can is 2.375 in., then what is the height of the can? (one fluid ounce equals approximately 1.8 cu/in.) : Find the cubic inches of the can 12 * 1.8 = 21.6 cu/in : Volume of a cylinder = V : Find the radius: 2.375/2 = 1.1875 in : = 21.6 = 21.6 : 4.43h = 21.6 h = h = 4.876 inches is the height : : Check on calc enter (pi*1.1875^2*4.876)/1.8 = 12.00 oz
 Numbers_Word_Problems/264507: one number is four greater than another number when three times the smaller number is added to twice the larger number the result is 43. Could you please give me the method to work it out i know the answer is 7 i just don't know how to get there.1 solutions Answer 194758 by ankor@dixie-net.com(15623)   on 2010-02-02 15:11:12 (Show Source): You can put this solution on YOUR website!let x = "one number" let y = "another number" : Write an equation for each statement: : "one number is four greater than another number" x = y + 4 : "when three times the smaller number is added to twice the larger number the result is 43" 3y + 2x = 43 : Replace x with (y+4), derived from the 1st statement 3y + 2(y+4) = 43 3y + 2y + 8 = 43 5y = 43 - 8 5y = 35 y = y = 7 : I'll let you find x
 Miscellaneous_Word_Problems/263906: s^2 = t^-1 and t^1/4 = u^-1/3, then what is the value of s in terms of u?1 solutions Answer 194576 by ankor@dixie-net.com(15623)   on 2010-02-01 21:10:30 (Show Source): You can put this solution on YOUR website!s^2 = t^-1 and t^1/4 = u^-1/3, then what is the value of s in terms of u : Reciprocal gets rid of the neg exponent then : : Raise both side to the 4th power ; (this is -4/3 power) : Replace t in Reciprocal gets rid of the neg exponent We can also write the square root like this which is ; (exponent is 2/3)
 Problems-with-consecutive-odd-even-integers/264106: One-fifth of sum of two consecutive integers is 19 less than the smaller integer. find the smaller of the two integers?1 solutions Answer 194523 by ankor@dixie-net.com(15623)   on 2010-02-01 19:11:29 (Show Source): You can put this solution on YOUR website!One-fifth of sum of two consecutive integers is 19 less than the smaller integer. find the smaller of the two integers? : Two consecutive integers: x, (x+1) : "One-fifth of sum of two consecutive integers is 19 less than the smaller" (x + (x+1)) = x - 19 Multiply both sides by 5 2x + 1 = 5x - 95 : 1 + 95 = 5x - 2x : 96 - 3x x = x = 32, the smaller integer ; : Check in original equation (32 + 33) = 32 - 19 (65) = 13
 Polynomials-and-rational-expressions/264010: I need help factoring polynomial of this question: bc+b+cd+d thank you!1 solutions Answer 194520 by ankor@dixie-net.com(15623)   on 2010-02-01 19:05:18 (Show Source): You can put this solution on YOUR website!bc + b + cd + d : Factor b, factor d b(c+1) + d(c+1) : Factor out (c+1) (c+1) (b+d)
 Polynomials-and-rational-expressions/264117: Help please! State any restrictions on x. And solve for x. 5 2 7 - + - = - 3x x^2 91 solutions Answer 194516 by ankor@dixie-net.com(15623)   on 2010-02-01 18:55:45 (Show Source): You can put this solution on YOUR website!solve for x. 5 2 7 - + - = - 3x x^2 9 : + = Multiply both sides by 9x^2, results : 3x(5) + 9(2) = x^2(7) : 15x + 18 = 7x^2 : A quadratic equation 0 = 7x^2 - 15x - 18 : Factors to: (7x + 6)(x - 3) = 0 : Two solutions x = 3 and 7x = -6 x = ; x cannot = 0 : Check solution using x=3 + =
 Mixture_Word_Problems/263609: How many liters of a 40%-alcohol solution must be mixed with 10 liters of a solution that is 80% alcohol to get a solution that is 60% alcohol?1 solutions Answer 194316 by ankor@dixie-net.com(15623)   on 2010-01-31 21:37:54 (Show Source): You can put this solution on YOUR website!How many liters of a 40%-alcohol solution must be mixed with 10 liters of a solution that is 80% alcohol to get a solution that is 60% alcohol? : let x = amt of 40% solution required : A typical mixture equation : .4x + .8(10) = .60(x+10) .4x + 8 = .6x + 6 8 - 6 = .6x - .4x 2 = .2x x = x = 10 liters of 40% solution required : : Check .4(10) + .8(10) = .6(10+10) 4 + 8 = .6(20)