If 54% of the town's 49,000 voters cast ballots the number of votes cast is:

(\( \frac{54}{100} \)) x 49,000 = \( \frac{2,646,000}{100} \) = 26,460

The mayor got 64% of the votes cast which is:

(\( \frac{64}{100} \)) x 26,460 = \( \frac{1,693,440}{100} \) = 16,934 votes.

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $200
i = 0.08 x $200

No payments were made so the total amount due is the original amount + the accumulated interest:

1

To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{32}{56} \) = \( \frac{\frac{32}{8}}{\frac{56}{8}} \) = \( \frac{4}{7} \)

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 5 and 9 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 9}{5 x 9} \) + \( \frac{3 x 5}{9 x 5} \)

\( \frac{63}{45} \) + \( \frac{15}{45} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{63 + 15}{45} \) = \( \frac{78}{45} \) = 1\(\frac{11}{15}\)