Calculating list size from original and altered average when x is removed.

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The average of x number of values is 66, and when a certain 77 is removed from these values, the average drops to 62. Find x, or the number of values that when averaged give 66, and when 77 is removed from the list x, the new average is 62. What is x, no need to find the values.

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Let the sum of $x$ values be $S$. Then the average is $$\frac{S}{x} = 66.$$ That if $77$ is deducted the new average is $62$ means $$\frac{S-77}{x-1} = 62.$$ Combining these two equations yields $$\frac{4x-15}{x-1}=0.$$ From here we can say that $x\neq 1$ and $x$ is not an integer.