Rearrange the product
(5.91 * 10^(-3)) * (8.7 * 10^10)
as
(5.91 * 8.7) * (10^(-3) * 10^10)
We have 5.91 * 8.7 = 51.417, and 10^(-3) * 10^10 = 10^(10 - 3) = 10^7, so the original product above reduces to
51.417 * 10^7
We can "add" powers of 10 by moving the decimal place to the left:
51.417 = 5.1417 * 10
so that
51.417 * 10^7 = (5.1417 * 10) * 10^7 = 5.1417 * 10^8
The strategy for winning every time appears to be to ensure that the remaining number of coins is a multiple of 6. Then the first player can ensure a win by taking 2 coins to make the total number be 48.
⅝ of the votes were for blue. That leaves ⅜ of the votes remaining. 5/9 of the remaining ⅜ votes were for green, so you multiply 5/9 x ⅜ = 15/72 votes for green. ⅝ of the votes were for blue, so you can multiply the fraction by 9/9 to get 45/72. So 45/72 votes were for blue, and 15/72 votes were for green. That leaves 12/72 votes remaining, which were for red. Since the question says 48 votes out of the total number of votes were for red, this means 48/v = 12/72 (v = the total number of votes). Cross multiply and solve for v to get v = 288. The fraction for blue is ⅝, so you can say x/288 = ⅝ (x = the number of votes for blue). Cross multiply and solve for x to get x = 180 votes for blue.
