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 Miscellaneous_Word_Problems/161212: toms uncle owns a triangular piece of land. the perimeter fence that surrounds the land measures 378 yards. the shortest side is 30 yards longer than one-half of the longest side. the second longest side is 2 yards shorter than the longest side. what is the length of each side?1 solutions Answer 118753 by ankor@dixie-net.com(15638)   on 2008-10-09 16:17:47 (Show Source): You can put this solution on YOUR website!the fence measures 378 yards. the shortest side is 30 yards longer than one-half of the longest side. the second longest side is 2 yards shorter than the longest side. what is the length of each side? : Let x = the longest side : from the statements, "the shortest side is 30 yards longer than one-half of the longest side." we can say: .5x + 30 = the shortest side and " the second longest side is 2 yards shorter than the longest side." x-2 = 2nd longest side ; what is the length of each side? : Solve for x: x + (.5x+30) + (x-2) = 378 x + .5x + x + 30 - 2 = 378 2.5x + 28 = 378 2.5x = 378 - 28 2.5x = 350 x = x = 140 yds is the longest side then .5(140) + 30 = 100 yd is the shortest side and 140 - 2 = 138 yds is the 2nd side : : Check: 140 + 100 + 138 = 378
 Numbers_Word_Problems/161194: a girl buys three apples and seven oranges for \$4.56. if an orange costs \$0.28 more than an apple, how much does each fruit cost?1 solutions Answer 118750 by ankor@dixie-net.com(15638)   on 2008-10-09 15:53:21 (Show Source): You can put this solution on YOUR website!a girl buys three apples and seven oranges for \$4.56. if an orange costs \$0.28 more than an apple, how much does each fruit cost? : Let x = cost for an apple Then (x+.28) = cost for an orange (given information) : Write an equation for the statement: "girl buys three apples and seven oranges for \$4.56." 3x + 7(x+.28) = 4.56 : 3x + 7x + 1.96 = 4.56 : 3x + 7x = 4.56 - 196 : 10x = 2.60 : x = x = .26 is the cost for an apple then .26 + .28 = .54 cost for an orange : : Check solution in original equation: 3(.26) + 7(.54) = .78 + 3.78 = 4.56
 Miscellaneous_Word_Problems/161117: A 24-hour digital clock displays the hours and minutes throughout the course of a day. Such times as 2:42 and 13:31 are palindromic. What is the longest time lapse between successive palindromic times? Please help me, kind tutor, I am in desperate need of your help. Thank you so much!1 solutions Answer 118733 by ankor@dixie-net.com(15638)   on 2008-10-09 12:23:06 (Show Source): You can put this solution on YOUR website! 24-hour digital clock displays the hours and minutes throughout the course of a day. Such times as 2:42 and 13:31 are palindromic. What is the longest time lapse between successive palindromic times? : No one seems to want to do this, here is my effort, not positive about it, but perhaps it will get you thinking in the right direction : Note that digits 6,7,8,9 do not occur in the minute's 10's digit position : From 1:01 to 1:51 every 10 min From 1:51 to 2:02 = 11 min From 2:02 to 2:52 every 10 min From 2:52 to 3:03 = 11 min From 3:03 to 3:53 every 10 min From 3:53 to 4:04 = 11 min Same until you get to: 9:59: From 9:59 to 1001 = 2 min From 1001 to 1111 = 1 hr 10 min From 1111 to 1221 = 1 hr 10 min same until you get 1551: 1551 to 2002 4 hrs 11 min, this is the longest time 2002 to 2112 1 hr 10 min 2112 to 2222 1 hr 10 min 2222 to 2332 1 hr 10 min 2332 to 1:01 1 hr 29 min
 Quadratic_Equations/161020: Extreme hardship. Kim starts to walk 3 mi to school at 7:30 A.M. with a temperature of 0°F. Her brother Bryan starts at 7:45 A.M. on his bicycle, traveling 10 mph faster than Kim. If they get to school at the same time, then how fast is each one traveling?1 solutions Answer 118666 by ankor@dixie-net.com(15638)   on 2008-10-08 20:09:44 (Show Source): You can put this solution on YOUR website!Kim starts to walk 3 mi to school at 7:30 A.M. with a temperature of 0°F. Her brother Bryan starts at 7:45 A.M. on his bicycle, traveling 10 mph faster than Kim. If they get to school at the same time, then how fast is each one traveling? : Change 15 min to hrs: 15/60 = .25 hrs : Let s = K's walking speed then (s+10) = B's biking speed : Write a time equation: Time = : K's travel time = B's travel time + .25 hr = + .25 : Multiply equation by t(t+10) to get rid of the denominator, results 3(s+10) = 3s + .25(s(s+10) : 3s + 30 = 3s + .25s^2 + 2.5s Arrange as a quadratic equation on the right 0 = .25s^2 + 2.5s + 3s - 3s - 30 : .25s^2 + 2.5s - 30 = 0 Get rid of those decimals, mult equation by 4, results s^2 + 10s - 120 = 0 : Use the quadratic formula to solve for s: In this equation a=1, b=10, c=-120 : solve this you should get a postive solution of: s = 7.05 mph is K's walking speed then 7.05 + 10 = 17.05 mph is B's biking speed : : Confirm this by finding the time of each 3/7.05 = .425 hrs or 25.5 min 3/17.05 = .176 hrs or 10.6 min --------------- Difference ~ 15 min
 Evaluation_Word_Problems/161028: two less than one third of a number equals 3 more than fourth of the number. find the number1 solutions Answer 118654 by ankor@dixie-net.com(15638)   on 2008-10-08 17:53:40 (Show Source): You can put this solution on YOUR website!two less than one third of a number equals 3 more than fourth of the number. find the number x - 2 = x + 3 Add 2 to both sides: x = x + 3 + 2 x = x + 5 Multiply equation by 12 to get rid of the denominators: 12*x = 12* x + 12(5) Results: 4x = 3x + 60 4x - 3x = 60 x = 60 : : Check solution original equation: (60) - 2 = (60) + 3 20 - 2 = 15 + 3
 Evaluation_Word_Problems/161029: twice the greater of two consecutive odd integers is 13 less than three times the lesser number. find the integers1 solutions Answer 118653 by ankor@dixie-net.com(15638)   on 2008-10-08 17:48:02 (Show Source): You can put this solution on YOUR website!Let the two odd consecutive integers be: x, (x+2) Write an equation for what it says: "twice the greater of two consecutive odd integers is 13 less than three times the lesser number." 2(x+2) = 3x - 13 2x + 4 = 3x - 13 4 + 13 = 3x - 2x 17 = x : The two numbers, 17, 19 : Check solution in the given statement 2(19) = 3(17) - 13 38 = 51 - 13
 Numeric_Fractions/161003: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM: Simplify the complex fraction. x/x+1/9/x^2-11 solutions Answer 118642 by ankor@dixie-net.com(15638)   on 2008-10-08 15:47:53 (Show Source): You can put this solution on YOUR website!Assume you mean: ----------- : Remember the rule dividing fractions,"Invert the dividing fraction and multiply" * : x^2-1 is a the "difference of squares"; factor that * : Cancel the (x+1)'s x * =
 Evaluation_Word_Problems/160902: A photograph that measures 20 cm by 35 cm is to be surrounded by a matte before framing. The width of the matte will be equal on all four sides. If the area of the matte will be twice the area of the photograph, determine the width of the matte.1 solutions Answer 118641 by ankor@dixie-net.com(15638)   on 2008-10-08 15:17:21 (Show Source): You can put this solution on YOUR website!A photograph that measures 20 cm by 35 cm is to be surrounded by a matte before framing. The width of the matte will be equal on all four sides. If the area of the matte will be twice the area of the photograph, determine the width of the matte. : Let x = width of the matte : 20 * 35 = 700 sq cm is the area of the photo then 2(700) = 1400 sq cm is the area of the matte : The dimension of the matte will be (2x+20) by (2x+35) : I am assuming that the matte will not be behind the photo, just around it Therefore we can find the area using these dimensions, assuming the area will be 2100 sq cm with 700 sq cm (which is behind the photo) not counted giving us a matte area of 1400 sq cm : (2x + 20) * (2x + 35) = 2100 FOIL 4x^2 + 70x + 40x + 700 = 2100 : 4x^2 + 110x + 700 - 2100 = 0 : 4x^2 + 110x - 1400 = 0 Simplify divide by 2 2x^2 + 55x - 700 = 0 This equation requires the quadratic formula: In this equation; a=2; b=55; c=-700 : : Solve this and you should get a positive solution: x = 9.4677 cm as the width ; A rough check using a calc: 2x = 19 (20+19*)(35+19) = 2106 cm - 700 (behind the photo) = 1406 sq/cm area of the matte
 Rate-of-work-word-problems/160986: One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together? Thanks for your help! J1 solutions Answer 118636 by ankor@dixie-net.com(15638)   on 2008-10-08 14:18:58 (Show Source): You can put this solution on YOUR website!One person can do a job in 8 hours. A second person can do it in 12 hours. If the first person works 2 hours less than the second, how many hours will it take them working together? : Let t = time that they worked together then (t+2) = total time worked by the 2nd person : Let the completed job = 1 ; Each will do a fraction of the work which will add up to 1: : 1st person + 2nd person = completed job + = 1 : Multiply equation by 24 to get rid of the denominator, rsults: 3t + 2(t+2) = 24 3t + 2t + 4 = 24 3t + 2t = 24 - 4 5t = 20 t = t = 4 hrs working together ; : Check solution: 4/8 + 6/12 = 1
 Age_Word_Problems/160921: Obie told Beth I am twice as old as you were when I was as old as you are. Their ages told 49. How old is each.1 solutions Answer 118634 by ankor@dixie-net.com(15638)   on 2008-10-08 14:04:07 (Show Source): You can put this solution on YOUR website!Obie told Beth I am twice as old as you were when I was as old as you are. Their ages told 49. How old is each. : Let A = O's age now Let B = Beth's age now : A + B = 49 B = (49-A) : Write an equation for this statement: "Obie told Beth I am twice as old as you were when I was as old as you are." A = 2(B - (A-B)) A = 2(B - A + B A = 2(2B-A) A = 4B - 2A A + 2A = 4B 3A = 4B Substitute (49-A) for B 3A = 4(49-A) 3A = 196 - 4A 3A + 4A = 196 A = A = 28 yrs old is O's age Then 49 - 28 = 21 yrs is B's age : See if that fits the statement: Obie told Beth I am twice as old as you were when I was as old as you are. 28 = 2(21 - 7) 28 = 2(14)
 Word_Problems_With_Coins/160966: Amanda has some pennies, nickels, dimes, and quarters in her piggy bank. There is more than \$1.50 and less than \$2.25. Using the clues, determine how much money Amanda has. -there are 4 times as many nickels as quarters -there are twice as many quarters as dimes -there is an equal number of pennies and dimes Thank you for you help!!1 solutions Answer 118631 by ankor@dixie-net.com(15638)   on 2008-10-08 13:37:28 (Show Source): You can put this solution on YOUR website!Amanda has some pennies, nickels, dimes, and quarters in her piggy bank. There is more than \$1.50 and less than \$2.25. Using the clues, determine how much money Amanda has. : Write an equation for each statement: : "-there are 4 times as many nickels as quarters" n = 4q : "-there are twice as many quarters as dimes" q = 2d : "-there is an equal number of pennies and dimes" p = d : Write a total\$ equation within the given range .01p + .05n + .10d + .25q = 2.00 : try to get everything in terms of d: In the 1st equation, substitute 2d or q (from the 2nd equation) n = 4(2d) n = 8d : Substitute: .01d + .05(8d) + .10d + .25(2d) = 2.00 .01d + .40d + .10d + .50d = 2 1.01d = 2 d = obviously not a solution (has to be an integer) : Make a solution by multiplying 1.01 * 2, so the total is \$2.02, then we have: d = d = 2 dimes then .01(2) + .40(2) + .10(2) + .50(2) = 2 .02 + .80 + .20 + 1.00 = \$2.02 : Find the number of each coin using d = 2: p = d; 2 pennies n = 8d: 16 nickels d = 2 dimes q = 2d; 4 quarters ; : Confirm solution from this: .01(2) + .05(16) + .10(2) + .25(4) = .02 + .80 + .20 + 1.00 = \$2.02 is Amanda's total : There are probably other ways to do this. Did this make sense to you?
 Circles/160972: My worksheet says: In a circle whose diameter is 20 inches, a chord is 6 inches from the center. What is the length of the chord?1 solutions Answer 118628 by ankor@dixie-net.com(15638)   on 2008-10-08 13:02:36 (Show Source): You can put this solution on YOUR website!In a circle whose diameter is 20 inches, a chord is 6 inches from the center. What is the length of the chord? : Here is one way. Draw a circle, draw in the chord. See that a triangle is formed by length of the chord and two radii. : This triangle consists of two right triangles where: hypotenuse = 10" (radius) one side = 6" distance from chord to the center one side = 1/2 the length of the chord (x) : x^2 + 6^2 = 10^2 x^2 + 36 = 100 x^2 = 100 - 36 x = x = 8" is half the chord, therefore the chord = 16"
 Numbers_Word_Problems/160793: The tens digit of a three-digit number exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit. When the digits are reversed, the new number exceeds the original number by 198. Find the original number.1 solutions Answer 118627 by ankor@dixie-net.com(15638)   on 2008-10-08 12:48:32 (Show Source): You can put this solution on YOUR website!The tens digit of a three-digit number exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit. When the digits are reversed, the new number exceeds the original number by 198. Find the original number. : Let x=100's digit; y=10's digit; z=units digit : "The tens digit of a three-digit number exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit." The equation for this statement: y - x = z - y y + y = x + z 2y = x+z ; "When the digits are reversed, the new number exceeds the original number by 198." 100z + 10y + x - (100x + 10z + z) = 198 100z + 10y + x - 100x - 10z - z = 198 100z - z + 10y - 10y + x - 100x = 198 99z - 99x = 198 Divide equation by 99: z - x = 2 z = x + 2 :: In the 1st equation substitute (x+2) for z 2y = x + (x+2) 2y = 2x + 2 Divide equation by 2 y = x + 2 x = y - 2 : y has to > 2, (x can't = 0) try y = 3, use the two equations to find x and z original number: 133, reverse number 331 331 - 133 = 198 : Find the original number. Here are some more numbers that will work y=4; 442 - 244 = 198 y=5; 553 - 355 = 198 y=6; 664 - 466 = 198 y=7; 775 - 577 = 198 y=8; 886 - 688 = 198 y=9; 997 = 799 = 198
 Travel_Word_Problems/160740: This question is from textbook a train leaves the station at 6:00pm traveling west at 80 mi/h. on a parallel track, a second train leaves the station 3 hours later traveling west at 100mi/h. at what time will the second train catch up with the first?1 solutions Answer 118590 by ankor@dixie-net.com(15638)   on 2008-10-07 21:39:07 (Show Source): You can put this solution on YOUR website!a train leaves the station at 6:00pm traveling west at 80 mi/h. on a parallel track, a second train leaves the station 3 hours later traveling west at 100mi/h. at what time will the second train catch up with the first? : Let t = travel time of the 1st train then (t-3) = travel time of the 2nd train : When the 2nd train catches the 1st train, they will have traveled the same distance : Write a distance equation: Dist = speed * time : 2nd train dist = 1st train dist 100(t-3) = 80t : 100t - 300 = 80t : 100t - 80t = +300 : 20t = 300 t = t = 15 hrs, travel time of the 1st train then 6 PM + 15 hrs = 9 AM on the following day : : Check the solution by confirming that both trains traveled ths same distance 80*15 = 1200 mi 100*12 = 1200 mi
 Age_Word_Problems/160883: Mary is six years older than her only brother Jaun. Three times Mary's age is 8 more than four times Juan's age. How old is Mary's brother? 3x = 8 + 4x (this is what I got out of this please help me figure this equation out once I figure it out I can solve on my own). Thanks1 solutions Answer 118580 by ankor@dixie-net.com(15638)   on 2008-10-07 20:46:38 (Show Source): You can put this solution on YOUR website!Mary is six years older than her only brother Jaun. Three times Mary's age is 8 more than four times Juan's age. How old is Mary's brother? Do it like this write an equation for each statement: "Mary is six years older than her only brother Jaun. M = J + 6 : "Three times Mary's age is 8 more than four times Juan's age." 3M = 4J + 8 : How old is Mary's brother? From the 1st equation, replace M with (J+6) in the above equation 3(J+6) = 4J + 8 3J + 18 = 4J + 8 18 - 8 = 4J - 3J J = 10 ; Use the 1st equation to find M, check solution in the 2nd equation
 Quadratic_Equations/160792: Please help me solve this problem Thanking you in advance.1 solutions Answer 118578 by ankor@dixie-net.com(15638)   on 2008-10-07 20:37:09 (Show Source): You can put this solution on YOUR website! : you have to use the quadratic formula to solve this: : In this equation: a=1; b=8; c=3 Solve this, two neg non-integer solutions
 Linear_Equations_And_Systems_Word_Problems/160789: please help me solve the problem. Thank you! the units digits of a two-digit number is 3 more than twice the tens digit. If the digits are reversed, the new number is 9 less than 4 times the original number. Find the original number.1 solutions Answer 118575 by ankor@dixie-net.com(15638)   on 2008-10-07 20:25:33 (Show Source): You can put this solution on YOUR website!the units digits of a two-digit number is 3 more than twice the tens digit. If the digits are reversed, the new number is 9 less than 4 times the original number. Find the original number. ; Let x = the 10's digit Let y - units digit then 10x + y = original number : Write and equation for each statement: ; "the units digits of a two-digit number is 3 more than twice the tens digit." y = 2x + 3 : "If the digits are reversed, the new number is 9 less than 4 times the original number." 10y + x = 4(10x+y) - 9 10y + x = 40x + 4y - 9 10y - 4y = 40x - x - 9 6y = 39x - 9 : Find the original number. : Substitute (2x+3) for y in the above equation: 6(2x+3) = 39x - 9 12x + 18 = 39x - 9 18 + 9 = 39x - 12x 27 = 27x x = 1 : Then using y = 2x+3 y = 2(1) + 3 y = 5 : Original number = 15 : : Check solution in the statement: "If the digits are reversed, the new number is 9 less than 4 times the original number." 51 = 4(15) - 9