Question 190156
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Let us assigned the two numbers be <font color=blue>x</font> & <font color=blue>y</font>.


1st condition:


The difference is 10: {{{x-y=10}}}


2nd condition:


One-sixth of sum is 11: {{{(1/6)(x+y)=11}}}


In 1st condition we get, {{{x=10+y}}}, subst. in 2nd condition:


{{{(1/6)(highlight(10+y)+y)=11}}}
{{{(1/6)(10+2y)=11}}}
{{{10/6+2y/6=11}}} ---> {{{cross(10)5/cross(6)3+cross(2)1y/cross(6)3=11}}}
{{{(1/3)y=11-5/3=(33-5)/3=28/3}}}
{{{cross(1/3)y/cross(1/3)=(28/3)/(1/3)=(28/cross(3))(cross(3)/1)}}}
{{{red(y=28)}}} ---> One number


Then, {{{x=10+28=red(38)}}} ---> The other number



Check via 2nd condition:
{{{(1/6)(38+28)=11}}}
{{{(1/6)(66)=11}}}
{{{11=11}}}


Thank you,
Jojo</font>