SOLUTION: The sum of three whole numbers between 0 and 10 is 16. The product of the numbers 120. The sum of the two smaller numbers equals the greatest number. What are the the numbers?

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Question 721839: The sum of three whole numbers between 0 and 10 is 16. The product of the numbers 120. The sum of the two smaller numbers equals the greatest number. What are the the numbers?
Answer by solver91311(24713) (Show Source):
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If the product of the three numbers is 120, since 120 ends in 0, one of the three numbers must be either 5 or 10. If one of the numbers is 10, then the product of the other 2 is 12 and they must add up to 10. No such numbers. So one of the numbers has to be 5. Dividing 120 by 5 is 24. The two single digit factors of 24 are either 4 and 6 or 3 and 8. No combination of 4, 5, and 6 exists where the sum of two of the digits is the third. But 3, 5, and 8 work because 3 plus 5 is 8. Recap: 3 + 5 + 8 = 16. 3 * 5 * 8 = 120. and 3 + 5 = 8. All conditions satisfied.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it