Question 1189945
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(1) Using formal algebra....<br>
{{{(7+x)/(17+x)=6/11}}}
{{{11(7+x)=6(17+x)}}}
{{{77+11x=102+6x}}}
{{{5x=25}}}
{{{x=5}}}<br>
ANSWER: 5<br>
(2) Using logical reasoning and simple mental arithmetic....<br>
The difference between the numerator and denominator in the given fraction 7/17 is 10.  When the same number is added to both numerator and denominator, that difference stays the same.<br>
So we need to find a fraction equivalent to 6/11 in which the difference between the numerator and denominator is 10.<br>
The difference between the numerator and denominator in the fraction 6/11 is 5; if we double the numerator and denominator, the difference will be 10, as we need. So<br>
{{{(6/11)*(2/2)+12/22 = (7+5)/(17+5)}}}<br>
ANSWER: 5<br>