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QThe numerator of a fraction is 10 less than the denominator

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.
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1 answers.
#1TristanAnswered at 2013-01-24 03:53:26
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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