The numerator of a fraction is 10 less than the denominator. If 4 is added to each, the value of the resulting fraction is 3/5. Find the original fraction.

I've tried using multiples of 3/5 and subtracting 4 from the numerator and denominator hoping it will give me a solution where the numerator is 10 less than the denominator but I want a faster way of figuring this problemo ut just in case I ever get it on a test.

I've tried using multiples of 3/5 and subtracting 4 from the numerator and denominator hoping it will give me a solution where the numerator is 10 less than the denominator but I want a faster way of figuring this problemo ut just in case I ever get it on a test.

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1 answers.

You could use this approach:
Let d = the denominator.
{{{((d-10)+4)/(d+4) = 3/5}}} Simplify then cross-multiply.
{{{(d-6)/(d+4) = 3/5}}}
{{{5(d-6) = 3(d+4)}}} Simplify and solve for d.
{{{5d-30 = 3d+12}}} Subtract 3d from both sides.
{{{2d-30 = 12}}} Add 30 to both sides.
{{{2d = 42}}} Divide both sides by 2.
d = 21
The original fraction is:
{{{(d-10)/d}}} or
{{{(21-10)/21}}}
{{{11/21}}} This is the original fraction.
Check:
Adding 4 to the numerator and to the denominator, we get:
{{{(11+4)/(21+4) = 15/25 = 3/5}}}

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