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algebra intermediate

Problem

The sum of three numbers ,, is 165. When the smallest number is multiplied by 7, the result is . The value is obtained by subtracting 9 from the largest number . This number also results by adding 9 to the third number . What is the product of the three numbers?
Solution
We are given , . Solving the last three equations for , , and , respectively, and substituting into the first equation, we have , which implies . Therefore, the three numbers are 11, 68, and 86. The product of 11, 68, and 86 is .
Final answer
64,\!328