NEED HELP IN ALGEBRA PLEASE SOLVE THIS DIGIT WORD PROBLEMS!
[From: ] [author: ] [Date: 11-10-06] [Hit: ]
and its 12 less than 4 times the reciprocal of the second. that means2/x +12 =4/y-------------------eqn. 1 => 4/y-2/x =121/x +1/y=9 ------------------eqn 2 which is given in the problemnow solve the two equations.you will get4x - 2y = 12xy or, 2x -y = 6xyand, x +y = 9xyadd the two equations:by adding you will get----3x =15xyy=1/5and substitute the value of y in any one of the equations and you will get the value of x-2nd number (y) in terms of 1st number (x)—2 equations:1/x + 1/y = 9y + x = 9xy9xy - y = xy(9x - 1) = xy = x/(9x - 1)2(1/x) = 4(1/y) - 122/x = (4 - 12y)/y2y = 4x - 12xyy = 2x - 6xy6xy + y = 2xy(6x + 1) = 2xy = 2x/(6x + 1)1st number:x/(9x - 1) = 2x/(6x + 1)6x² + x = 18x² - 2x12x² = 3x4x = 1x = 1/42nd number (y)= (1/4)/(9[1/4] - 1)= (1/4)/([9 - 4]/4)= 1/4(4/5)= 4/20 or 1/5Answer: 1/4 & 1/5 are the numbers.......
on solving you get: y=1/5
on substitution in any eq. you get: x = 1/4
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ok so lets say that the two numbers are x and y
sum of their reciprocal means
= 1/x +1/y which is equals 9
twice the first number = 2/x as x is the first number. and its 12 less than 4 times the reciprocal of the second. that means
2/x +12 =4/y-------------------eqn. 1 => 4/y-2/x =12
1/x +1/y=9 ------------------eqn 2 which is given in the problem
now solve the two equations.
you will get
4x - 2y = 12xy or, 2x -y = 6xy
and, x +y = 9xy
add the two equations:
by adding you will get----
3x =15xy
y=1/5
and substitute the value of y in any one of the equations and you will get the value of x
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2nd number (y) in terms of 1st number (x)—2 equations:
1/x + 1/y = 9
y + x = 9xy
9xy - y = x
y(9x - 1) = x
y = x/(9x - 1)
2(1/x) = 4(1/y) - 12
2/x = (4 - 12y)/y
2y = 4x - 12xy
y = 2x - 6xy
6xy + y = 2x
y(6x + 1) = 2x
y = 2x/(6x + 1)
1st number:
x/(9x - 1) = 2x/(6x + 1)
6x² + x = 18x² - 2x
12x² = 3x
4x = 1
x = 1/4
2nd number (y)
= (1/4)/(9[1/4] - 1)
= (1/4)/([9 - 4]/4)
= 1/4(4/5)
= 4/20 or 1/5
Answer: 1/4 & 1/5 are the numbers.
Check:
2(4) = 4(5) - 12
8 = 20 - 12
8 = 8
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1/ x + 1/ y = 9
2/x + 12 = 4/y
1 / x + 1/y = 9
MULTIPLY BY xy
y + x = 9xy (A)
2/x - 4/y = -12
MULTIPLY BY xy
2y - 4x = -12xy
y - 2x = - 6xy (B)
(A) - (B) = 3x = 15xy
15y = 3
y = 3/15 = 1/5
1/x + 1/1/5 = 9
1/x = 4
x = 1/4
ANSWER = 1/4 and 1/5
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let x be the first nos reciprocal
let y be the second nos reciprocal
then;
x+y=9 ------> x = 9 - y
and
2x+12=4y
substituting x;
2(9-y)+12=4y
y=5
x=4
two nos are
1/5 and 1/4
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