The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.

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 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.

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

\( \frac{2 x 7}{6 x 7} \) + \( \frac{5 x 3}{14 x 3} \)

\( \frac{14}{42} \) + \( \frac{15}{42} \)

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

\( \frac{14 + 15}{42} \) = \( \frac{29}{42} \) = \(\frac{29}{42}\)

To add these radicals together their radicands must be the same:

6\( \sqrt{80} \) + 4\( \sqrt{5} \)
6\( \sqrt{16 \times 5} \) + 4\( \sqrt{5} \)
6\( \sqrt{4^2 \times 5} \) + 4\( \sqrt{5} \)
(6)(4)\( \sqrt{5} \) + 4\( \sqrt{5} \)
24\( \sqrt{5} \) + 4\( \sqrt{5} \)

Now that the radicands are identical, you can add them together:

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{4}{5} \) x \( \frac{1}{5} \) = \( \frac{4 x 1}{5 x 5} \) = \( \frac{4}{25} \) = \(\frac{4}{25}\)

You have 12 out of the total of 300 raffle tickets sold so you have a (\( \frac{12}{300} \)) x 100 = \( \frac{12 \times 100}{300} \) = \( \frac{1200}{300} \) = 4% chance to win the raffle.