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 Numbers_Word_Problems/511264: My number has 3 different digits, and all of them are even. This is divisibale by 5 and 8. The sum of its digits is greater than12.1 solutions Answer 342308 by ankor@dixie-net.com(15747)   on 2011-10-08 22:05:53 (Show Source): You can put this solution on YOUR website!My number has 3 different digits, and all of them are even. This is divisibale by 5 and 8. The sum of its digits is greater than12. : How about 680?
 Miscellaneous_Word_Problems/511387: a number consists of two digits the digits in the ten's place is 3 times the digit in the unit place if 54 is subtracted from the number the digits are reversed . The number is1 solutions Answer 342261 by ankor@dixie-net.com(15747)   on 2011-10-08 16:31:31 (Show Source): You can put this solution on YOUR website!a number consists of two digits the digits in the ten's place is 3 times the digit in the unit place if 54 is subtracted from the number the digits are reversed. The number is : Let the two digit number = 10x + y : "the ten's place is 3 times the digit in the unit place" x = 3y : "if 54 is subtracted from the number the digits are reversed." 10x + y - 54 = 10y + x 10x - x = 10y - y + 54 9x = 9y + 54 simplify, divide by 9 x = y + 6 Replace x with 3y 3y = y + 6 3y - y = 6 2y = 6 y = 3 then x = 3(3) x = 9 : 93 is the number : : Check solution in the statement: "if 54 is subtracted from the number the digits are reversed." 93 - 54 = 39
 Age_Word_Problems/511286: A man is 4 years older than his wife and 5 times as old as his son. When the son was born, the age of the wife was six-sevenths that of her husband's age. Find the age of each.1 solutions Answer 342204 by ankor@dixie-net.com(15747)   on 2011-10-08 10:33:05 (Show Source): You can put this solution on YOUR website!A man is 4 years older than his wife and 5 times as old as his son. When the son was born, the age of the wife was six-sevenths that of her husband's age. Find the age of each. : Write an equation for each statement: : "A man is 4 years older than his wife" m = w + 4 subtract 4 from both sides w = (m-4) : "and 5 times as old as his son." m = 5s : "When the son was born, the age of the wife was six-sevenths that of her husband's age." w - s = (m-s) multiply both sides by 7 7(w-s) = 6(m-s) 7w - 7s = 6m - 6s 7w = 6m - 6s + 7s 7w = 6m + s replace w with (m-4) 7(m-4) = 6m + s 7m - 28 = 6m + s 7m - 6m = s + 28 m = s + 28 replace m with 5s 5s = s + 28 5s - s = 28 4s = 28 s = 7 yrs is the son's age then 5(7) = 35 yrs is Dad's age and 35-4 = 31 yrs is Mom's age : ; confirm these solutions in the statement: "When the son was born, the age of the wife was six-sevenths that of her husband's age." 31 - 7 = (35 - 7) 24 = *28 24 = 24;
 Rate-of-work-word-problems/511281: A man and a boy perform a task in 2 days. They completed one half of the task the first day with the man working 8 hours and the boy working 10 hours. On the next day, they finished the task with the man working 4 hours and the boy working 15 hours. Find how many hours would take for each to do the task working alone.1 solutions Answer 342199 by ankor@dixie-net.com(15747)   on 2011-10-08 09:48:35 (Show Source): You can put this solution on YOUR website!A man and a boy perform a task in 2 days. They completed one half of the task the first day with the man working 8 hours and the boy working 10 hours. On the next day, they finished the task with the man working 4 hours and the boy working 15 hours. Find how many hours would take for each to do the task working alone. : Let m = time required by the man working alone let b = time required by the boy working alone Let the completed job = 1 : 1st day equation: + = 2nd day equation: + = : multiply the 2nd equation by 2, subtract the 1st equation + = 1 + = ------------------- eliminates m, find b = b = 2(20) b = 40 hrs, boy alone : Find m + = reduce fraction + = multiply by 4m 4(8) + m = 2m 32 = 2m - m m = 32 hrs, man alone : : Confirm this using the 2nd day equation + = + =
 Travel_Word_Problems/511072: If you walked 7 1/4 miles at a rate of 2 1/2 miles per hour, how long in hours and minutes will it take to complete the walk?1 solutions Answer 342198 by ankor@dixie-net.com(15747)   on 2011-10-08 09:19:17 (Show Source): You can put this solution on YOUR website!If you walked 7 1/4 miles at a rate of 2 1/2 miles per hour, how long in hours and minutes will it take to complete the walk? : = 2.9 hrs, 2 + .9(60) = 2 hrs 54 min
 Proportions/511040: if a certain amount of food will last 50 days for 200 soldiers, how long will it last if 50 soldiers are added at the end of 20 days?1 solutions Answer 342130 by ankor@dixie-net.com(15747)   on 2011-10-07 22:08:13 (Show Source): You can put this solution on YOUR website!if a certain amount of food will last 50 days for 200 soldiers, how long will it last if 50 soldiers are added at the end of 20 days? : 50 * 200 = 10000 food days, total available food : Let d = no. of days for this scenario 200d + 50(d-20) = 10000 200d + 50d - 1000 = 10000 250d = 10000 + 1000 250d = 11000 d = 44 days
 Linear-equations/511027: Will you please help me solve this equation? 2x+4=28 Thank you.:)1 solutions Answer 342121 by ankor@dixie-net.com(15747)   on 2011-10-07 21:56:54 (Show Source): You can put this solution on YOUR website!2x + 4 = 28 Subtract 4 from both sides 2x = 28 - 4 2x = 24 divide both sides by 2 x = x = 12 : : Confirm this by replacing x with 12 in the original equation 2(12) + 4 = 28
 Numbers_Word_Problems/511030: I am a 4 digit whole number my digits decrease by 2 from the thousand place to the ones place each of my digits is an even number . what number am i ? 1 solutions Answer 342117 by ankor@dixie-net.com(15747)   on 2011-10-07 21:51:01 (Show Source): You can put this solution on YOUR website!I am a 4 digit whole number a, b, c, d : my digits decrease by 2 from the thousand place to the ones place a, (a-2), (a-4), (a-6), (a-6) each of my digits is an even number . what number am i ? a has to be 8, then the number is: 8642
 Distributive-associative-commutative-properties/511029: 7=-2x+71 solutions Answer 342116 by ankor@dixie-net.com(15747)   on 2011-10-07 21:48:39 (Show Source): You can put this solution on YOUR website!7 = -2x + 7 subtract 7 from both sides 0 = -2x therefore x = 0
 Triangles/511010: The largest angle of a triangle is 6 times the smallest angle and it is 3 times the other angle. Find the size of the smallest angle. A. 40 degrees B. 30 degrees C. 20 degrees D. 10 degrees So far I have tried all answers but they don't come to 180 degrees. My first thought was 30 degrees because then the other angle would be 90 but then that would require the largest angle to be 180. Now there is a 200 degree triangle but I am not sure if I am correct. All help would be greatly appreciated! Thank you, Ann1 solutions Answer 342114 by ankor@dixie-net.com(15747)   on 2011-10-07 21:42:26 (Show Source): You can put this solution on YOUR website!Let A = the largest angle Let B = the "other angle let C = the smallest angle : Write an equation for each statement, get them all in terms of A: : "The largest angle of a triangle is 6 times the smallest angle" A = 6C Divide both sides by 6, and we have C = A : and it is 3 times the other angle. A = 3B Divide both sides by 3 B = A : A + B + C = 180 therefore A + A + A = 180 Get rid of those annoying fractions, multiply by 6 and we have 6A + 2A + A = 6(180) 9A = 1080 A = A = 120 degrees is the largest angle : Find the size of the smallest angle. C = A C = *120 C = 20 degrees : : You can check this; find the other angle and ensure they add up to 180
 Age_Word_Problems/511004: hi i need help with this kind of word problem because i dont understand it i would really appreciate it if you can also show the work so i can understand it more thank you kristine, jake, and lexi are cousins. jake is 2 years older than kristine and lexi is 8 years younger than jake. the sum of their ages is 35. find lexi's age. thanks again!1 solutions Answer 342113 by ankor@dixie-net.com(15747)   on 2011-10-07 21:28:46 (Show Source): You can put this solution on YOUR website!kristine, jake, and lexi are cousins. Write an equation for each statement : jake is 2 years older than kristine j = k + 2 we want to get k in terms of j, like the next equation, subtract 2 from both sides and we can write it k = j - 2 : lexi is 8 years younger than jake. l = j - 8 : the sum of their ages is 35. k + j + l = 35 Replace k with (j-2) and l with (j-8) (j-2) + j + (j-8) = 35 combine like terms 3j - 10 = 35 3j = 35 + 10 3j = 45 j = j = 15 yr is Jake's age : Find L's age l = 15 - 8 l = 7 yrs is Lexi's age : : You should check this by finding k's age and see that the sum of all three ages add up 35
 Linear_Equations_And_Systems_Word_Problems/510894: two girls each have a different number of candies. jasmine said if you give me 5 i will have as many you. Wendy said if you give me 5 i will have twice as many as you.how many candies did each girl have? 1 solutions Answer 342103 by ankor@dixie-net.com(15747)   on 2011-10-07 20:41:11 (Show Source): You can put this solution on YOUR website!Let j = original no. Jasmine had let w = original no. Wendy had : two girls each have a different number of candies. : "jasmine said if you give me 5 i will have as many you." j + 5 = w - 5 j = w - 5 - 5 j = w - 10 : Wendy said if you give me 5 i will have twice as many as you w + 5 = 2(j-5) w + 5 = 2j - 10 w = 2j - 10 - 5 w = 2j - 15 replace j with (w-10) w = 2(w-10) - 15 w = 2w - 20 - 15 w - 2w = -35 -w = -35 w = 35 candies had Wendy then j = 35 - 10 j = 25 candies had Jasmine : Check and see that this is true in both statements
 Numbers_Word_Problems/510994: one half the sum of a givin number and six is the same as ten decreased by the difference obtained when five is subtracted from the number. find the number1 solutions Answer 342101 by ankor@dixie-net.com(15747)   on 2011-10-07 20:27:44 (Show Source): You can put this solution on YOUR website!one half the sum of a given number and six is the same as ten decreased by the difference obtained when five is subtracted from the number. find the number : Solve this equation (n+6) = 10 - (n-5) : (n+6) = 10 - n + 5 : (n+6) = 15 - n multiply both sides by 2 n + 6 = 2(15-n) you should be able to finish this, check your solution in the original equation
 Percentage-and-ratio-word-problems/511287: The numerator and denominator of a fraction are together equal to 100. Increase the numerator by 18 and decrease the denominator by 16 and the fraction is doubled. What is the fraction?1 solutions Answer 342100 by ankor@dixie-net.com(15747)   on 2011-10-07 20:11:48 (Show Source): You can put this solution on YOUR website!The numerator and denominator of a fraction are together equal to 100. n + d = 100 d = (100-a) : Increase the numerator by 18 and decrease the denominator by 16 and the fraction is doubled. = Cross multiply d(n+18) = 2n(d-16) dn + 18d = 2dn - 32n 18d = 2dn - dn - 32n 18d = dn - 32n : replace d with (100-n) 18(100-n) = n(100-n) - 32n 1800 - 18n = 100n - n^2 - 32n : Arrange as a quadratic equation on the left n^2 - 18n -100n + 32n + 1800 = 0 n^2 - 86n + 1800 = 0 : You can use the quadratic formula here but it will factor to: (n-50){n-36) = 0 Two solutions (remember n + d = 100) n = 50, then d = 50, but of course 50/50 = 1, not really considered a fraction and n = 36, then d = 64 : is the fraction we want, reduces to : : Check this in the original equation: = reduces to: twice the original fraction
 Exponents/510926: My question is when doing a problem example, 10x-22=29-7x . I under stand that I need to get my X on one side of the equation and I do that by adding or subracting on both sides. How do you know witch side to pick. and wether to add or subract? 10x-22= 29-7x -7x 29 3x -51 = -10x -51 divid each by 10 x= 5.1 Thank you 1 solutions Answer 342056 by ankor@dixie-net.com(15747)   on 2011-10-07 15:58:27 (Show Source): You can put this solution on YOUR website!10x-22=29-7x Generally we want it on the left, but it is not necessary, sometimes it's easier to select the side which will make x positive (the final solution, x has to be positive) : add 7x to both sides, that gets rid of x on the right side 10x + 7x - 22 = 29 -7x +7x 17x - 22 = 29 : add 22 to both sides, that gets the numbers on the right side 17x - 22 + 22 = 29 + 22 17x = 51 ; Divide both sides by 17 to get 1x x = x = 3 : : See if this works out in the original equation, replace x with 3 10(3) - 22 = 29 - 7(3) 30 - 22 = 29 - 21 8 = 8; equality reigns, x=3 is correct!
 Travel_Word_Problems/510833: plane A is 40 miles south and 100 miles east of plane B. plane A is flying 2 miles west for ever mile it flies north, while plane B is flying 3 miles east for every mile it flies south. where do there paths cross? 1 solutions Answer 342053 by ankor@dixie-net.com(15747)   on 2011-10-07 15:43:15 (Show Source): You can put this solution on YOUR website!plane A is 40 miles south and 100 miles east of plane B. plane A is flying 2 miles west for ever mile it flies north, while plane B is flying 3 miles east for every mile it flies south. where do there paths cross? : Write a linear equation for the line taken by each plane With O origin, Plane B: When x = 0, y = 40 "plane B is flying 3 miles east for every mile it flies south." Using the rise/run rule the slope will be -1/3 (negative because it's moving southward) y = -x + 40 : Plane A: x intercept = +100, find the y intercept "plane A is flying 2 miles west for ever mile it flies north," Slope = -1/2; find the y intercept (b) (100) + b = 0 -50 + b = 0 b = 50 the equation for A: y = -x + 50, plot this with B intercept x=60 mi east, y=20 mi north
 Age_Word_Problems/510937: Matthew is 3 times as old as Jenny. In 7 years he will be twice as old as she will be then. How old is each now. I have figured out the answer, but not how to work the problem. I tried: x + 1/3X = 2 times X + 7 + 1/3 X + 7 which is completely wrong. I have not done a problen where I didn't have a specific number for an answer. Reid 1 solutions Answer 341940 by ankor@dixie-net.com(15747)   on 2011-10-06 22:04:56 (Show Source): You can put this solution on YOUR website!Matthew is 3 times as old as Jenny. m = 3j In 7 years he will be twice as old as she will be then. m + 7 = 2(j+7) m + 7 = 2j + 14 m = 2j + 14 - 7 m = 2j + 7 Replace m with 3j 3j = 2j + 7 3j - 2j = 7 j = 7 yrs then obviously m = 21 yrs
 Rectangles/510709: THE POPULATION OF TWO TOWNS ARE CHANGING AT STEADY RATES. ONE TOWN HAS A POPULATION OF 25,500. ITS POPULATION IS INCREASING BY 200 PEOPLE EACH YEAR. THE OTHER TOWN HAS A POPULATION OF 47,900. ITS POPULATION IS DECREASING BY 800 PEOPLE EACH YEAR. IF THE RATE FOR EACH TOWN REMAINS THE SAME,IN HOW MANY YEARS WILL THE POPULATION BE THE SAME ? 1 solutions Answer 341930 by ankor@dixie-net.com(15747)   on 2011-10-06 21:46:35 (Show Source): You can put this solution on YOUR website!THE POPULATION OF TWO TOWNS ARE CHANGING AT STEADY RATES. ONE TOWN HAS A POPULATION OF 25,500. ITS POPULATION IS INCREASING BY 200 PEOPLE EACH YEAR. THE OTHER TOWN HAS A POPULATION OF 47,900. ITS POPULATION IS DECREASING BY 800 PEOPLE EACH YEAR. IF THE RATE FOR EACH TOWN REMAINS THE SAME,IN HOW MANY YEARS WILL THE POPULATION BE THE SAME ? : let t = no. of years for this to happen An equation for the 1st town f(t) = 200t + 25500 An equation for the 2nd town f(t) = -800t + 47900 : Find when the populations are equal 1st town = 2nd town 200t + 25500 = -800t + 47900 200t + 800t = 47900 - 25500 1000t = 22400 t = t = 22.4 yrs the will be the same : : Check this by finding the population of each after 22.4 yrs 200(22.4) + 25500 = 29980 -800(22.4)+ 47900 = 29980
 Proportions/510705: It took 2 hours for 1 person to sweep the yard. How long would it take 4 persons working at the same speed to do the same job? My attempt: Firstly, it has to take less than 2 hours since the number of persons has been increased. The # of persons has been increased by 3 so: Increase in persons/ Time = 3 / 2 1.5 hours. 1 solutions Answer 341925 by ankor@dixie-net.com(15747)   on 2011-10-06 21:34:43 (Show Source): You can put this solution on YOUR website!It took 2 hours for 1 person to sweep the yard. How long would it take 4 persons working at the same speed to do the same job? : Assume they each had broom, and worked at the same rate (2hrs to complete the job) : Let t = time required by 4 men doing the job Let the completed job = 1 : Each will do a fraction of the job, and the fractions will add up to 1 + + + = 1 Multiply thru by 2 t + t + t + t = 2 4t = 2 t = t = hr with all 4 men sweeping