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Question

The sum of three numbers is 98. The ratio of the first to the second is 23, and the ratio of the second to the third is 58. The second number is:

Accepted Answer

Let the 3 numbers be a, b, and c. We see that a+b+c = 98 and ab = 23 3a = 2b bc = 58 8b = 5c Writing a and c in terms of b we have a = 23 b and c = 85 b. Substituting in the sum, we have 23 b + b + 85 b = 98 4915 b = 98 b = 98 1549 b = 30 30