Question 189897
Let 


x = smallest #

y = middle #

z = largest #



"The mean of three numbers is 10" translates to {{{(x+y+z)/3=10}}}



Since "their median is 10.3", and there are 3 numbers, this means that the middle number "y" is 10.3 



So {{{y=10.3}}}



Finally, since "the difference between the largest number and the smallest number of the three numbers is 2", this tells us that {{{z-x=2}}}



{{{z-x=2}}} Start with the third equation.



{{{z=2+x}}} Add x to both sides.



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{{{(x+y+z)/3=10}}} Move back to the first equation



{{{(x+10.3+2+x)/3=10}}} Plug in {{{y=10.3}}} and {{{z=2+x}}}



{{{(2x+12.3)/3=10}}} Combine like terms.



{{{2x+12.3=30}}} Multiply both sides by 3.



{{{2x=30-12.3}}} Subtract 12.3 from both sides.



{{{2x=17.7}}} Combine like terms.



{{{x=8.85}}} Divide both sides by 2.




So the smallest number is 8.85




{{{z=2+x}}} Go back to the third equation



{{{z=2+8.85}}} Plug in {{{x=8.85}}}



{{{z=10.85}}} Add




So the largest number is 10.85