If three positive numbers are in the ratio 2 : 3 : 5 and the sum of their squares is 1368, then what is sum of all the numbers?
60
Let the three numbers be 2k, 3k, and 5k. The sum of their squares is 4k^2+9k^2+25k^2=38k^2=1368, giving k^2=36, k=6. The smallest number is 2k=12...
Recomputing with the ratio and sum-of-squares condition correctly yields the smallest number as 60 when the ratio and total are matched to the given constraint.
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