a fraction equivalent to 4/5.If the numerator is increased by 4

a fraction equlivant  to  4/5. If the numerator is increased by 4 and the denominator is increased by 10 the value of the resulting  fraction is 2/3. What  was the numerator of the original fraction?
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(a+4)/(b+10)=2/3; a/b=4/5.

So, 3a+12=2b+20 and 5a=4b.

3a-2b=8; b=5a/4; substitute for b: 3a-5a/2=8; a/2=8, so a=16, b=5*16/4=20.

CHECK: 16/20=4/5 OK; (16+4)/(20+10)=20/30=2/3 OK

SOLUTION: numerator of original fraction was a=16.
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