If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 5\8. If the numerator and denominator of the same fraction are each increased by 1, the fraction becomes 1\2. Find the fraction.
Answers
Answer:
8/15
Step-by-step explanation:
Suppose that the reqd. fraction is x/y.
Suppose that the reqd. fraction is x/y.Then, by the 1st condition (cond.), we have,
Suppose that the reqd. fraction is x/y.Then, by the 1st condition (cond.), we have,x+2/y+1=58⇒8x+16=5y+5,or,8x−5y+11=0...(1)
Suppose that the reqd. fraction is x/y.Then, by the 1st condition (cond.), we have,x+2/y+1=58⇒8x+16=5y+5,or,8x−5y+11=0...(1)Utilising the 2nd cond., we get x−1/y−1=12,i.e.,
Suppose that the reqd. fraction is x/y.Then, by the 1st condition (cond.), we have,x+2/y+1=58⇒8x+16=5y+5,or,8x−5y+11=0...(1)Utilising the 2nd cond., we get x−1/y−1=12,i.e.,2x−2=y−1,or,y=2x−1....(2)
Suppose that the reqd. fraction is x/y.Then, by the 1st condition (cond.), we have,x+2/y+1=58⇒8x+16=5y+5,or,8x−5y+11=0...(1)Utilising the 2nd cond., we get x−1/y−1=12,i.e.,2x−2=y−1,or,y=2x−1....(2)Sub.ing the value of y from (2) to (1), we have,
Suppose that the reqd. fraction is x/y.Then, by the 1st condition (cond.), we have,x+2/y+1=58⇒8x+16=5y+5,or,8x−5y+11=0...(1)Utilising the 2nd cond., we get x−1/y−1=12,i.e.,2x−2=y−1,or,y=2x−1....(2)Sub.ing the value of y from (2) to (1), we have,8x−5/(2x−1)+11=0.∴−2x+16=0.∴x=8.
Suppose that the reqd. fraction is x/y.Then, by the 1st condition (cond.), we have,x+2/y+1=58⇒8x+16=5y+5,or,8x−5y+11=0...(1)Utilising the 2nd cond., we get x−1/y−1=12,i.e.,2x−2=y−1,or,y=2x−1....(2)Sub.ing the value of y from (2) to (1), we have,8x−5/(2x−1)+11=0.∴−2x+16=0.∴x=8.Then by (2),y=2(8)−1=15.
Suppose that the reqd. fraction is x/y.Then, by the 1st condition (cond.), we have,x+2/y+1=58⇒8x+16=5y+5,or,8x−5y+11=0...(1)Utilising the 2nd cond., we get x−1/y−1=12,i.e.,2x−2=y−1,or,y=2x−1....(2)Sub.ing the value of y from (2) to (1), we have,8x−5/(2x−1)+11=0.∴−2x+16=0.∴x=8.Then by (2),y=2(8)−1=15.Thus, we get the desired fraction x/y=8/15.
Answer:
The fraction is 5/11
Step-by-step explanation:
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