Question 869793
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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 {{{(x + 2)/(y + 2) = 5/7}}}
i.e {{{7*(x + 2) = 5*(y + 2)}}}
Simplifying
{{{7*x - 5*y + 4 = 0}}} ----> (1)
The second statement tells us that {{{x / (y - 1) = 3/4}}}
i.e. {{{4*x = 3*y - 3}}}
Simplifying
{{{4*x - 3*y + 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.

*[invoke linear_substitution "x", "y", 7, -5, -4, 4, -3, -3 ]

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

Hope this helps :)
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