SOLUTION: if the average of three distinct positive intergers is 4 what is the greatest possible value for one of those integers a) 5 b) 6 c) 9 d) 11 e) 12

Question 461933: if the average of three distinct positive intergers is 4 what is the greatest possible value for one of those integers
a) 5
b) 6
c) 9
d) 11
e) 12
Found 2 solutions by robertb, math-vortex:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
c) 9.
Since the terms of the sum are all positive integers, then the least value any of the terms can take is 1. The second least positive integral value one of the remaining terms can take is 2. (Remember the value of the next term is distinct from the first, and hence higher.) The value of the remaining term must then be maximal, which is 12 - 1 - 2 = 9.
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
if the average of three distinct positive integers is 4 what is the greatest possible value for one of those integers.
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We are going to use the formula for the average of three numbers and work backwards to find the answer to your question.
.
We find the average of three distinct integers by finding their sum and dividing by three.
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Since we divide the sum by 3 and get 4 as the average, the sum of the integers must be 12. (12/3 = 4.) Notice how we're working backwards?
.
Now we have three distinct integers that add up to 12. We want to know what is the greatest possible value for one of them. If one integer is going to be as large as possible, the other two must be a small as possible. The two smallest positive integers are 1 and 2.
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Now we have 1 + 2 + [our mystery integer] = 12.
1 + 2 = 3, so our mystery integer must be 9. (9 + 3 = 12.)
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Hope this helps!
.
Ms. Figgy
math.in.the.vortex
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