SOLUTION: problem 1. the sum of the reciprocals of two numbers is 7. The larger reciprocal exceeds the smaller by 7/3. Find the numbers. problem 2. if the numerator and the denominator o

Question 350818: problem 1. the sum of the reciprocals of two numbers is 7. The larger reciprocal exceeds the smaller by 7/3. Find the numbers.
problem 2. if the numerator and the denominator of a certain fraction are both increased by 3, the resulting fractions equals 2/3. if the numerator and the denominator are both decreased by 2, the resulting fraction equals 1/2. determine the fraction.
problem 3. a certain fraction has a value 3/4. If its numerator is decreased by 7 and its denominator increased by 4, the resulting fraction has the value of 1/2. find the original fraction.
Found 2 solutions by mananth, sudhanshu_kmr:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
problem 1. the sum of the reciprocals of two numbers is 7. The larger reciprocal exceeds the smaller by 7/3. Find the numbers.
let x be one number
y be the other number
1/x + 1/y =7
x+y/xy=7
x+y=7xy.......................1
..
1/x-1/y = 7/3
y-x / xy = 7/3
3(y-x)=7xy
3y-3x=7xy .....................2
multiply 1 by 3 and add to 2
3x+3y = 21xy
Add
6y=28xy
x= 3/14
...
14/3 +1/y =7
1/y = 7 - 14/3
1/y =7/3
y = 3/7
Reciprocal of x & y when added = 7
problem 2. if the numerator and the denominator of a certain fraction are both increased by 3, the resulting fractions equals 2/3. if the numerator and the denominator are both decreased by 2, the resulting fraction equals 1/2. determine the fraction.
let the fraction be x/y
x+3/y+3 = 2/3
3(x+3)=2(y+3)
3x+9=2y+6
3x-2y=-3.....................1
x-2 / y-2 = 1/2
2(x-2)=y-2
2x-4 = y-2
2x-y = 2......................2
multiply equation 1 by -2 & equation 2 by 3
-6x+4y=6
6x-3y=6
y=12
plug value of y in equation 1
3x-24 =-3
3x=24-3
3x=21
x=7
problem 3. a certain fraction has a value 3/4. If its numerator is decreased by 7 and its denominator increased by 4, the resulting fraction has the value of 1/2. find the original fraction.
...
x/y = 3/4
x=3y/4.................1
x-7 / y+4 = 1/2
2(x-7)=y+4
2x-14=y+4
2x-y=18................2
plug value of x in equation 2
2*(3y/4)-y =18
3y/2-y =18
(3y-2y )/ 2 =18
y = 2*18
y=36
plug value of y in equation 1
2x-36=18
2x=36+18
2x=54
x=27
....
C H E C K
27/36 = 3/4
AAAh1
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!
1 Ans:
Let the numbers are x and y, where y is greater than x.
( 1/y will smaller than 1/x )
so, 1/x +1/y = 7 .......(1) and 1/x = 1/y +7/3 ........(2)
using (1) we got
x + y = 7xy
using (2) we got
3y-3x = 7xy

solving these two equations......
x= 3/14 y = 6/14

so, numbers are 3/14 and 6/14 .
................................................................................
2.Ans.
Let the fraction be x/y.
then according to question....
( x+3 )/(y+3) = 2/3 ..............(1)
and (x-2)/ (y-2) = 1/2 ............. (2)
using (1) we got 3x-2y = -3
using (2) we got 2x-y = 2
after solving these two equations. x =7, y =12.

so, the fraction is 7/12.

................................................................................
3 Ans.
Let the fraction be x/y.
so, x/y =3/4 ..........(1)
and (x-7) /(y+4) = 1/2 ......(2)

using (1) we got 4x - 3y =0
using (2) we got 2x - y =18
after solving these two equations. x =27 , y =36

so, fraction value is 27/36
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