Question 153291
Let x be the number.
One third of the result of twice a certain number plus one can be expressed as:
{{{(1/3)*2x+1)}}}
One quarter of twice the certain number can be expressed as:
{{{(1/4)*2x}}}
According to the given information, these two expressions are the same. So we have:
{{{(1/3)*2x+1=(1/4)*2x}}}
Solving for x, we have
{{{2x/3+1=x/2}}}
{{{6*(2x/3+1)=6(x/2)}}}   (multiply both sides by 6)
{{{4x+6=3x}}}
{{{x=-6}}}
So the number is -6.