Can someone help me with this math problem.10 pts to anyone who explainsthe best......?

Question

I am thinking of three different positive numbers.The greatest of them is twice a perfect square. The least of them is 1 less than half the greatest. The average of the three numbers is 12. Which three numbers am I thinking of???

plz show the work..............help!!!

Answer 1

three numbers must be three times 12, or 36 because thats their average

the three numbers add to 36, and the only perfect squares that go in are 4, 9, 16, and 25. i can eliminate 16 and 25 because twice those numbers is too high. Ill take 9. so i get 18, 8, and 10. That works. If u use 4. Then u get 8, 3, and 15 which doesnt work cause 8's gotta be the most.

So the answer is : 8, 10, and 18

Answer 2

"three different positive numbers"

a, b, c are integers such that 0 < a < b < c

"The average of the three numbers is 12."

(a+b+c)/3 = 12   ⇒   a < 12 < c  and a+b+c = 36

"The greatest of them is twice a perfect square."

2×1² = 2 ≯ 12

2×2² = 8 ≯ 12

2×3² = 18

2×4² = 32

c = 18 or 32

"The least of them is 1 less than half the greatest."

32/2 - 1 = 15 ≮ 12 so c≠32

∴c=18, a=8, b=10

Answer 3

18,8,10