The right answer is Option C : 5
Step-by-step explanation:
Let,
The numerator of fraction = x
The denominator of a fraction is 10 more than its numerator.
[tex]\frac{x}{x+10}[/tex]
When 1/3 is added to this fraction,
[tex]\frac{x}{x+10}+\frac{1}{3}[/tex]
the resulting fraction’s denominator is three times the denominator of the original fraction its numerator is 15 less than its denominator
[tex]\frac{3(x+10)-15}{3(x+10)}[/tex]
Therefore, it becomes
[tex]\frac{x}{x+10}+\frac{1}{3} = \frac{3(x+10)-15}{3(x+10)}[/tex]
Taking LCM on left side
[tex]\frac{3x+(x+10)}{3(x+10)}=\frac{(3x+30)-15}{3(x+10)}\\\\\frac{3x+x+10}{3(x+10)}=\frac{3x+30-15}{x(x+10)}\\\\\frac{4x+10}{3(x+10)}=\frac{3x+15}{3(x+10)}[/tex]
Multiplying both sides by 3(x+10)
[tex]3(x+10)*\frac{4x+10}{3(x+10)}=\frac{3x+15}{3(x+10)}*3(x+10)\\4x+10=3x+15\\4x-3x=15-10\\x=5[/tex]
The numerator of original fraction is 5.
The right answer is Option C : 5
Keywords: fraction, addition
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