Question 787247
"Shane added a number to one-sixth" translates to {{{x + 1/6}}}


"Chris subtracted the same number from one and two-thirds" translates to {{{1&2/3 - x}}} and because {{{1&2/3 = (1*3+2)/3 = 5/3}}}. So this means that {{{1&2/3 - x}}} is the same as {{{5/3 - x}}}


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"They each got the same answer." means that the two expressions are equal, so this means


{{{x + 1/6 = 5/3 - x}}}


{{{x + 1/6  + x= 5/3}}} Add x to both sides.


{{{x  + x= 5/3 - 1/6}}} Subtract 1/6 from both sides.


{{{x  + x= 10/6 - 1/6}}} Multiply 5/3 by 2/2.


{{{2x= 9/6}}} Combine like terms.


{{{2x= 3/2}}} Reduce


{{{x= (3/2)*(1/2)}}} Multiply both sides by 1/2 to isolate x


{{{x= (3*1)/(2*2)}}} 


{{{x= 3/4}}} 


Therefore, the number is {{{3/4}}}