SOLUTION: the value of a fraction is 3/4. when 7 is added to its numerator, the resulting fraction is equal to the reciprocal of the original fraction. find the orginal fraction

Click here to see ALL problems on Miscellaneous Word Problems

Question 283971: the value of a fraction is 3/4. when 7 is added to its numerator, the resulting fraction is equal to the reciprocal of the original fraction. find the orginal fraction
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let the original fraction be represented by . Since the value of the original fraction is , we can say that:

and

Hence the original fraction can be represented as:

Adding 7 to the numerator:

And we are given that this new fraction is equal to the reciprocal of the original fraction:

Cross-multiply:

Solving results in or

is an absurd result because you cannot have a fraction with a numerator of zero and a value different from zero, nor can you have a fraction with a denominator of zero in any case, so discard and retain

Hence:

And the original fraction is then:

This fraction does indeed have a value of and if you add 7 to the numerator you get the reciprocal of which also has a value of .

John