Problem: in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 4720 votes were polled , then how many valid votes did b get ?
Rationale: "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 4720 32.5 k = 32.5 k / 100 k * 4720 = 1534 the number of valid votes polled in favour of b is 1534 . answer : a"
annotated_formula: divide(subtract(multiply(subtract(const_1, divide(20, const_100)), 4720), divide(multiply(15, 4720), const_100)), const_2)