We can form an equation of the form below using the info in the question
3/10 + x * (7/10) = 1/2
Solving, we get x = 2/7
I think the trick here is "what percent of the leftover votes" not
"what percent of the total votes"
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jayhawk2001
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If total votes cast were x. Beth received 3x/10
Remainder votes cast = 7x/10
In order to receive ½ of the votes cast Beth needs total 5x/10 votes cast or 2x/10 additional votes
Thus she needs (2x/10)/(7x/10) more votes = 2/7
Remainder votes cast = 7x/10
In order to receive ½ of the votes cast Beth needs total 5x/10 votes cast or 2x/10 additional votes
Thus she needs (2x/10)/(7x/10) more votes = 2/7
