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# Recent problems solved by 'vidhyak'

vidhyak answered: 94 problems
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 Average/733757: What is the value of n in this equation? 45 - 5 + 80 + n = 2001 solutions Answer 448704 by vidhyak(94)   on 2013-04-05 02:06:30 (Show Source): You can put this solution on YOUR website!45 - 5 + 80 + n = 200 40 + 80 + n = 200 120 + n = 200 n = 200 - 120 = 80 n = 80
 Numbers_Word_Problems/733891: If three times the smaller of two consecutive integers is added to four times the larger, the result is 123. Find the smaller integer.1 solutions Answer 448703 by vidhyak(94)   on 2013-04-05 02:00:47 (Show Source): You can put this solution on YOUR website!Let the two consecutive integers be n, n+1. three times the smaller integer = 3n four times the larger integer = 4(n+1) 3n + 4(n+1) = 123 3n + 4n + 4 = 123 7n + 4 = 123 7n = 123 - 4 = 119 n = 119/7 =17 smaller integer is 17
 Rectangles/733955: the perimeter of a rectangle is 38 centimers. the length is 7.5 centimeters. what is the width?1 solutions Answer 448702 by vidhyak(94)   on 2013-04-05 01:40:17 (Show Source): You can put this solution on YOUR website!The perimeter of rectangle is 2(l+b) where l is the length and b is the width 2(l+b) = 38 2(7.5 + b) = 38 15 + 2b = 38 2b = 38 - 15 2b = 23 b = 11.5 Width is 11.5cm
 �t�e�s�t/734006: fill in the missing value, 23kg= mg is it 23,000,000 ,2300 are 0,231 solutions Answer 448701 by vidhyak(94)   on 2013-04-05 01:34:52 (Show Source): You can put this solution on YOUR website!1kg = 1,000,000 milligrams Therefore 23 kg = 23, 000,000 mg
 Numbers_Word_Problems/733647: if 4 is added to a number and the sum is tripled the result is 28 more than the number. find the number.1 solutions Answer 448700 by vidhyak(94)   on 2013-04-05 01:24:59 (Show Source): You can put this solution on YOUR website!Let the number be n if 4 is added to a number and the sum is tripled the result is 28 more than the number. 4 is added to the number and the sum is tripled 3 * ( n + 4) 3 * ( n + 4) = n + 28 Solving the equation 3n + 12 = n + 28 3n - n = 28 -12 2n = 16 n =8 Number is 8
 Equations/734033: what is 30-[9+4(8-5)]? 1 solutions Answer 448699 by vidhyak(94)   on 2013-04-05 01:04:34 (Show Source): You can put this solution on YOUR website!30-[9+4(8-5)] Start solving from innermost parenthesis 30-[9+4(3)] 30-[9+12] 30-21 9
 test/733137: M2+8m+71 solutions Answer 448310 by vidhyak(94)   on 2013-04-03 01:04:57 (Show Source): You can put this solution on YOUR website!M^2+8m+7 8m is split as m +7m m^2 + m + 7m +7 Group first two terms and last two terms together (m^2+M) + (7m + 7) m(m+1) + 7(m+1) take the common term m+1 (m+1)(m+7) M= -1, -7
 Numbers_Word_Problems/732711: The sum of the digits of a two digit number is 11. The original two-digit number is 5 more than 3 times the number with its digits reversed. Find the original number. 1 solutions Answer 448101 by vidhyak(94)   on 2013-04-02 11:00:59 (Show Source): You can put this solution on YOUR website!The sum of the digits of a two digit number is 11. The 2 digit numbers whose sum of digits add to 11 are 29, 38, 47, 56, 65, 74, 83, 92 The original two-digit number is 5 more than 3 times the number with its digits reversed From the above statement, it is understood that the original two-digit number is greater than the reversed number so the number should be either 65, 74, 83 or 92 original number = 5 + 3(reversed number) Let's apply the formula to 65, 74, 83, 92 to see which is correct 65 = 5 + 3(56) = 5 + 177 = 182 -------not correct 74 = 5 + 3(47) = 5 + 141 = 146 -------not correct 83 = 5 + 3(38) = 5 + 114 = 119 -------not correct 92 = 5 + 3(29) = 5 + 87 = 92 -------correct 92 is the number
 Graphs/732902: (5x-3y=16)(4x+5y=-2)1 solutions Answer 448096 by vidhyak(94)   on 2013-04-02 10:45:54 (Show Source): You can put this solution on YOUR website! 5x - 3y = 16......eq 1 4x + 5y = -2......eq 2 Multiply eq1 by 5 and eq2 by 3 to cancel out 'y' 25x - 15y = 80 12x - 15y = -6 Add the above equations 37x = 74 x = 2 Substitute x = 2 in eq 1 5x - 3y = 16 5(2) - 3y = 16 10 - 3y = 16 -3y = 16 - 10 -3y = 6 y = -2 x = 2, y = -2
 test/732857: 5x+3y=8, 8x-2y=61 solutions Answer 448095 by vidhyak(94)   on 2013-04-02 10:40:22 (Show Source): You can put this solution on YOUR website!5x + 3y = 8......eq 1 8x - 2y = 6......eq 2 Multiply eq1 by 2 and eq2 by 3 to cancel out 'y' 10x + 6y = 16 24x - 6y = 18 Add the above equations 34x = 34 x = 1 Substitute x = 1 in eq 1 5x + 3y = 8 5(1) + 3y = 8 5 + 3y = 8 3y = 8 - 5 3y = 3 y = 1 x = 1, y = 1
 Linear-systems/732871: x+9=121 solutions Answer 448093 by vidhyak(94)   on 2013-04-02 10:18:11 (Show Source): You can put this solution on YOUR website!x + 9 = 12 Keep the variable on one side and numbers on the other side x = 12 - 9 = 3 x = 3
 test/732848: Solve m2 - 16=01 solutions Answer 448092 by vidhyak(94)   on 2013-04-02 10:13:53 (Show Source): You can put this solution on YOUR website!m^2 - 16 = 0 m^2 = 16 Take squareroot on both sides m = +4, -4
 Age_Word_Problems/732880: The sum of a boy and his father's age is 63 years. The difference between their ages is 33 years....Translate the two statements and solve for each variable.1 solutions Answer 448091 by vidhyak(94)   on 2013-04-02 10:06:59 (Show Source): You can put this solution on YOUR website!Let boy's age be b Let father's age be f The sum of a boy and his father's age is 63 years f + b = 63 -----------------------eq. 1 The difference between their ages is 33 years f - b = 33 -----------------------eq. 2 Solving the 2 equations(Add the 2 equations) f + b = 63 f - b = 33 2f = 96 f = 96/2 = 48 Father's age is 48 Substitute f = 48 in eq 1 f + b = 63 48 + b = 63 b = 63 - 48 b = 15 Boy's age is 15 Father's age is 48
 Age_Word_Problems/732837: Percy is 8 years older than Ginny. In ten years time he will be three times Ginny's present age. How old is Percy now?1 solutions Answer 448088 by vidhyak(94)   on 2013-04-02 09:53:26 (Show Source): You can put this solution on YOUR website!Let Percy's age be p Let Ginny's age be g Percy is 8 years older than Ginny g + 8 = p -----------------------eq. 1 In ten years time he will be three times Ginny's present age In ten years Percy will be p + 10 yrs old Three times Ginny's age = 3g p + 10 = 3g --------------eq 2 Substitue eq1 in eq2 p + 10 = 3g g + 8 + 10 = 3g g + 18 = 3g 2g = 18 g = 9 Ginny's age is 9 years Substitute g = 9 in eq 1 g + 8 = p 9 + 8 = p P = 17
 Linear_Equations_And_Systems_Word_Problems/324538: The number of blues was 7 less than the sum or the whites and the greens. The number of greens was 1 greater than the sum of the blues and the whites. How many of each kind were there if there were three times as many greens as blues?1 solutions Answer 232975 by vidhyak(94)   on 2010-07-25 00:59:37 (Show Source): You can put this solution on YOUR website!Let the 3 colors be w,g,b for white, green and blue The number of blues was 7 less than the sum or the whites and the greens w + g -7 = b w + g - b = 7 ...... eq 1 The number of greens was 1 greater than the sum of the blues and the whites g = 1 + b + w b + w -g = -1 .........eq 2 three times as many greens as blues 3b = g ------eq 3 Substitute eq 3 in eq 1 w + g - b = 7 w + 3b - b = 7 w + 2b = 7 -------eq 4 Substitute eq 3 in eq 2 b + w - g = -1 b + w - 3b = -1 w - 2b = -1 .........eq5 Add eq4 and eq 5 w + 2b = 7 w - 2b = -1 2w = 6 w = 3 Substitute w = 3 in eq 4 to get the value of b w + 2b = 7 3 + 2b = 7 2b = 7-3 = 4 b = 2 Substitute w = 3, b = 2 in eq 1 to get the value of g w + g - b = 7 3 + g - 2 = 7 1 + g = 7 g = 6 There are 3 whites, 2 blues and 6 greens
 Geometry_Word_Problems/325291: the sum of twice one number and three times a second number is 84 sum of thrice the first number and five times the second is 136.what is the number? 1 solutions Answer 232973 by vidhyak(94)   on 2010-07-25 00:47:00 (Show Source): You can put this solution on YOUR website!Let the 2 numbers be x,y the sum of twice one number and three times a second number is 84 2x + 3y =84 ......eq 1 sum of thrice the first number and five times the second is 136 3x +5y =136 ......eq 2 Multiply eq1 by 3 and eq 2 by 2 to cancel out 'x' 6x + 9y =252 6x +10y =272 Subtract the above equations -y = -20 y = 20 Substitute y = 20 in eq 1 2x + 3y =84 2x + 3(20) =84 2x + 60 =84 2x =84 -60 2x = 24 x =12 x = 12, y = 20
 Equations/109896: i need a answer to: 3x-y=2 x+2y=101 solutions Answer 80101 by vidhyak(94)   on 2007-11-13 15:47:23 (Show Source): You can put this solution on YOUR website! 3x -y =2 ......eq 1 x +2y =10 ......eq 2 Multiply eq1 by 2 6x -2y =4 x +2y =10 Add the above equations 7x =14 x=2 Substitute x = 2 in eq 1 3x -y =2 3(2) -y =2 6 - y =2 -y = -4 y = 4 x = 2, y = 4
 Linear-systems/109905: Solve each of the following by substitution 5x-2y=-5 y-5x=3 Thanks for any help!!! Heather1 solutions Answer 80099 by vidhyak(94)   on 2007-11-13 15:43:17 (Show Source): You can put this solution on YOUR website!5x-2y=-5 y-5x=3 Rearranging the equation 5x -2y = -5 .......eq 1 -5x +y = 3 ....... eq 2 Adding Eq1 and eq2 you get -y = -2 y = 2 Substitute y = 2 in eq 1 oe eq 2 5x -2y = -5 5x -2(2) = -5 5x -4 = -5 5x = -1 x = -1/5
Age_Word_Problems/74272: Marivic is five years older than Michelle. In three years, the product of her age and Michelle's age five years ago will be 90 years. Find their present ages.
1 solutions

Answer 53371 by vidhyak(94)   on 2007-03-13 20:19:53 (Show Source):
You can put this solution on YOUR website!
Let Marivic's age be x
Let Michelle's age be y

Marivic is five years older than Michelle
x = y + 5 -----------------------eq. 1

In three years, the product of her age and Michelle's age five years ago will be 90 years
In three years marvic will be x + 3 yrs old
Michelle's age five years ago was y - 5 yrs old

(x + 3)(y - 5) = 90 --------------eq 2

Substitue eq1 in eq2
(y + 5 + 3) (y - 5) = 90
(y + 8) (y - 5) = 90
y^2 + 3y -40 = 90
y^2 + 3y -130 = 0

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=529 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 10, -13. Here's your graph:

Answers for y= 10,-13
Age is a positive integer, so Michelle's age is 10

x = y + 5
x= 15
so Marivic's age is 15

 Equations/74159: This question is from textbook Pre-Algebra The difference between twice a number and 9 is 16.Find the number?1 solutions Answer 53191 by vidhyak(94)   on 2007-03-12 17:04:07 (Show Source): You can put this solution on YOUR website!Let the number be x The difference between twice a number and 9 is 16 2x - 9 = 16 2x = 16 + 9 = 25 x = 12.5
 Linear_Equations_And_Systems_Word_Problems/41840: twice the sum of 4 and some number is 34 what is the number could some please help i am stuck thank you mike1 solutions Answer 27005 by vidhyak(94)   on 2006-06-12 21:52:05 (Show Source): You can put this solution on YOUR website!Let the number be x 2(4 + x) = 34 4 + x = 34/2 = 17 x = 17 - 4 = 13
Radicals/41356: Solve by using quadratice formula: 3x^2=11x+4
1 solutions

Answer 26982 by vidhyak(94)   on 2006-06-12 15:29:55 (Show Source):
You can put this solution on YOUR website!
3x^2 = 11x + 4
3x^2 - 11x - 4 = 0
3x^2 - 12x + x - 4 = 0
3x(x - 4) + 1(x - 4) = 0
(3x + 1)(x - 4)=0
x = -1/3, 4

Using the formula
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=169 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4, -0.333333333333333. Here's your graph:

 Equations/41677: This question is from textbook Algebra & Trigonometry square route 1 + x3 = 31 solutions Answer 26979 by vidhyak(94)   on 2006-06-12 13:38:52 (Show Source): You can put this solution on YOUR website!square route (1 + x^3 )= 3 Square on both sides 1 + x^3 = 3^2 1 + x^3 = 9 x^3 = 8 x = 2
 Geometric_formulas/27160: Mount Everest is the tallest mountain in the world. It is 237 meters higher than K2the second talest mountain. If the sum of their heights is 17,459 meters how tal is each mountain? How do I write the formula for this?1 solutions Answer 26777 by vidhyak(94)   on 2006-06-09 19:57:41 (Show Source): You can put this solution on YOUR website!The numbers were truncated in the above solution, so writing the equations x + x + 237 = 17459 2x + 237 = 17459 2x = 17222 x = 8611
 expressions/41459: 18=9-(3-x) show work1 solutions Answer 26776 by vidhyak(94)   on 2006-06-09 19:49:26 (Show Source): You can put this solution on YOUR website!18 = 9 -(3 - x) 18 = 9 -3 + x 18 = 6 + x x= 12
 Equations/41480: This question is from textbook algebra a introductory course plz help me solve this asap a.write a formula for the cost,c,of borrowing a book from a lending library for d days if the cost for the first 3 days is 25 cents and the cost for each additional day is 5 cents. b.find the cost of borrowing a book for a week.1 solutions Answer 26774 by vidhyak(94)   on 2006-06-09 19:45:16 (Show Source): You can put this solution on YOUR website!a) Cost for 3 days is 25 cents i.e., 3*.25 = .75 Cost for 4 days is 0.75 + 0.05 = 0.80 Cost for 5 days is 0.75 + 0.05 + 0.05 = 0.85 ... Formula would be c = 0.05(d-3) + 0.75 if the days are >=3 Formula would be c = 0.25d if the days is < 3 (i.e., 1 or 2 days) ------------------------------------------------ b) Substitute d = 7 in the above formula c = 0.05(d-3) + 0.75 c = 0.05(7-3) + 0.75 c = 0.20 + 0.75 c = 0.95 ( 95 cents)
 Age_Word_Problems/41479: ann's age is seven-tenths of Bill's age. In 4 years Ann's age will be eight-elevenths of Bill's age. How old is Bill now? The Ten's digit of a two-digit number is 3 more than the unit's digit. The number is 8 more than six times the sum of the digits. Find the number.1 solutions Answer 26773 by vidhyak(94)   on 2006-06-09 19:34:54 (Show Source): You can put this solution on YOUR website!Let Ann's age be A and Bill's age be B ann's age is seven-tenths of Bill's age. A = 7/10(B) ....eq1 In 4 years Ann's age will be eight-elevenths of Bill's age. A + 4 = 8/11(B+4).....eq2 Substitute eq1 in eq2 (7/10(B)) + 4 = 8/11(B+4) Cross multiply 11(7B + 40) = 80(B + 4) 77B + 440 = 80B + 320 -3B = -120 B=40 Bill's age is 40 ----------------------------------------------------- Let the ten digit be T and units digit U The number will be 10T + U The Ten's digit of a two-digit number is 3 more than the unit's digit. T = 3 + U .....eq1 The number is 8 more than six times the sum of the digits. 10T + U = 8 + 6(T + U) 10T + U = 8 + 6T + 6U 10T + U - 6T - 6U = 8 4T - 5U = 8 SUBSTITUTE T = 3 + U 4(3 + U) - 5U = 8 12 + 4U -5U =8 -U = -4 U = 4( UNIT'S DIGIT IS 4) Since Ten's digit is 3 more than the unit's digit, it 7 Number is 74
 Polynomials-and-rational-expressions/41165: I don't quite understand this one. Find a value for k so that 9m^2 - kn^2 will have the factors 3m + 7n, and 3m - 7n. Thanks1 solutions Answer 26683 by vidhyak(94)   on 2006-06-08 11:25:09 (Show Source): You can put this solution on YOUR website!Find a value for k so that 9m^2 - kn^2 will have the factors 3m + 7n, and 3m - 7n. (a + b)(a-b) = a^2 - b^2 The factors are 3m + 7n, and 3m - 7n. Let's apply the above formula a = 3m and b = 7n (3m + 7n)(3m - 7n) = 9m^2 - 49n^2 Comparing 9m^2 - 49n^2 with 9m^2 - kn^2, we get k = 49
 Expressions-with-variables/41166: 3[2+v]-4v=v+161 solutions Answer 26682 by vidhyak(94)   on 2006-06-08 11:21:11 (Show Source): You can put this solution on YOUR website!3[2+v] - 4v = v + 16 6 + 3v -4v -v -16 = 0 -2v - 10 = 0 -2v = 10 v = -5
 Linear-equations/41320: I need help figuring 5x + 8 + 3x - x + 5 = 6x - 31 solutions Answer 26681 by vidhyak(94)   on 2006-06-08 11:16:49 (Show Source): You can put this solution on YOUR website!5x + 8 + 3x - x + 5 = 6x - 3 5x + 8 + 3x - x + 5 - 6x + 3 = 0 x + 16 = 0 x = -16
 Distributive-associative-commutative-properties/41323: b+(b+5)-2(b-5)=18+b solve show work1 solutions Answer 26680 by vidhyak(94)   on 2006-06-08 11:14:55 (Show Source): You can put this solution on YOUR website!b + (b+5) -2(b-5) = 18 + b b + b + 5 -2b + 10 - 18 - b = 0 -b -3 = 0 b = -3