To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

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

\( \frac{9 x 5}{6 x 5} \) + \( \frac{8 x 3}{10 x 3} \)

\( \frac{45}{30} \) + \( \frac{24}{30} \)

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

\( \frac{45 + 24}{30} \) = \( \frac{69}{30} \) = 2\(\frac{3}{10}\)

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 $500
i = 0.07 x $500
i = $35

The amount of flour you need is (2 - 1\(\frac{1}{2}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{16}{8} \) - \( \frac{12}{8} \)) cups
\( \frac{4}{8} \) cups
\(\frac{1}{2}\) cups

If the tiger has consumed 30 pounds of food in 6 days that's \( \frac{30}{6} \) = 5 pounds of food per day. The tiger needs to consume 55 - 30 = 25 more pounds of food to reach 55 pounds total. At 5 pounds of food per day that's \( \frac{25}{5} \) = 5 more days.

If 37% of the town's 47,000 voters cast ballots the number of votes cast is:

(\( \frac{37}{100} \)) x 47,000 = \( \frac{1,739,000}{100} \) = 17,390

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

(\( \frac{64}{100} \)) x 17,390 = \( \frac{1,112,960}{100} \) = 11,130 votes.