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The sum of three whole numbers is 27. The mean of the three whole numbers is 9, and the greatest number is twice the least number.

What is the greatest number?

1 Answer

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Answer:

12

Explanation:

Let x be the smallest number, and y be the middle number. Then the largest number is 2x and the sum is ...

x + y + 2x = 27 ⇒ y = 27 -3x

The requirement that the middle number is y gives rise to the inequality ...

x < y < 2x

Substituting for y, we have ...

x < 27 -3x < 2x

Adding 3x gives us ...

4x < 27 < 5x

These two inequalities give us the requirement that ...

27/5 < x < 27/4

5.4 < x < 6.75

The only whole number in that range is x = 6. So, the greatest number is 2×6 = 12.

The greatest number is 12.

User Amin Golmahalleh
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