SOLUTION: The mean of three numbers is 10, and their median is 10.3. If the difference between the largest number and the smallest number of the three numbers is 2, what are the three numbe

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Question 189897: The mean of three numbers is 10, and their median is 10.3. If the difference between the largest number and the smallest number of the three numbers is 2, what are the three numbers?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let

x = smallest #
y = middle #
z = largest #


"The mean of three numbers is 10" translates to %28x%2By%2Bz%29%2F3=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%2Bx Add x to both sides.


-----------------------------


%28x%2By%2Bz%29%2F3=10 Move back to the first equation


%28x%2B10.3%2B2%2Bx%29%2F3=10 Plug in y=10.3 and z=2%2Bx


%282x%2B12.3%29%2F3=10 Combine like terms.


2x%2B12.3=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%2Bx Go back to the third equation


z=2%2B8.85 Plug in x=8.85


z=10.85 Add



So the largest number is 10.85