In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 12 workers at the company now and that's enough to staff 4 crews so there are \( \frac{12}{4} \) = 3 workers on a crew. 8 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 8 x 3 = 24 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 24 - 12 = 12 new staff for the busy season.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{88}{6} \) = 14\(\frac{2}{3}\)

So, it will take 14 full vans and one partially full van to transport the entire team making a total of 15 vans.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.

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

\( \frac{5 x 5}{9 x 5} \) + \( \frac{2 x 3}{15 x 3} \)

\( \frac{25}{45} \) + \( \frac{6}{45} \)

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

\( \frac{25 + 6}{45} \) = \( \frac{31}{45} \) = \(\frac{31}{45}\)

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

8\( \sqrt{75} \) + 7\( \sqrt{3} \)
8\( \sqrt{25 \times 3} \) + 7\( \sqrt{3} \)
8\( \sqrt{5^2 \times 3} \) + 7\( \sqrt{3} \)
(8)(5)\( \sqrt{3} \) + 7\( \sqrt{3} \)
40\( \sqrt{3} \) + 7\( \sqrt{3} \)

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