The numerator and denominator of a fraction are in the ratio 3:2. If 3 is added to the numerator and 2 is subtracted from the denominator a new fraction is formed whose value is 9/4. Find the original fraction.
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Let the fraction be x/y.
The numerator and denominator of a fraction are in the ratio 3:2.
=> x/y=3/2
=> x = (3y/2)
If 3 is added to the numerator and 2 is subtracted from the denominator a new fraction is formed whose value is 9/4.
=> (x + 3)/(y - 2)=9/4
Substitute x with using the new equation to form one equation with only one variable. Solve for that equation.
=> (3y/2 + 3)/(y - 2) = 9/4
=> (1.5y + 3)/(y - 2) = 2.25
=> y = 10
Plug x in (1).
=> x = (3y/2)
=> x = 15
Hence, the fraction is 15/10 = 3/2.
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