SOLUTION: if the numinator and denominatar of a fracrion is increased by 2 the fraction become 5/7 and if its denominator is decreased by 1 the fraction becomes 3/4 . find the fraction ?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: if the numinator and denominatar of a fracrion is increased by 2 the fraction become 5/7 and if its denominator is decreased by 1 the fraction becomes 3/4 . find the fraction ?      Log On


   

Question 869793: if the numinator and denominatar of a fracrion is increased by 2 the fraction become 5/7 and if its denominator is decreased by 1 the fraction becomes 3/4 . find the fraction ?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
if the numinator and denominatar of a fracrion is increased by 2 the fraction become 5/7 and if its denominator is decreased by 1 the fraction becomes 3/4 . find the fraction ?
Ans:
Let the fraction be x/y
The first statement tells us that %28x+%2B+2%29%2F%28y+%2B+2%29+=+5%2F7
i.e 7%2A%28x+%2B+2%29+=+5%2A%28y+%2B+2%29
Simplifying
7%2Ax+-+5%2Ay+%2B+4+=+0 ----> (1)
The second statement tells us that x+%2F+%28y+-+1%29+=+3%2F4
i.e. 4%2Ax+=+3%2Ay+-+3
Simplifying
4%2Ax+-+3%2Ay+%2B+3+=+0 -----> (2)
The set of 2 simultaneous equations (1) and (2) can be solved using the solver available in this site, as shown below.



 
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION


Solve:
  +system%28+%0D%0A++++7%5Cx+%2B+-5%5Cy+=+-4%2C%0D%0A++++4%5Cx+%2B+-3%5Cy+=+-3+%29%0D%0A++We'll use substitution. After moving -5*y to the right, we get:
  7%2Ax+=+-4+-+-5%2Ay, or x+=+-4%2F7+-+-5%2Ay%2F7. Substitute that
  into another equation:
  4%2A%28-4%2F7+-+-5%2Ay%2F7%29+%2B+-3%5Cy+=+-3 and simplify: So, we know that y=5. Since x+=+-4%2F7+-+-5%2Ay%2F7, x=3.
  
  Answer: system%28+x=3%2C+y=5+%29.
  



We get the solution as x = 3, y = 5
Hence the fraction is highlight%283%2F5%29
Check: Adding 2 to numerator and denominator, we get 5/7
Subtracting 1 from denominator, the fraction becomes 3/4. Correct!

Hope this helps :)