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. 6 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 6 x 3 = 18 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 18 - 12 = 6 new staff for the busy season.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 12 share.

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

\( \frac{2 x 3}{4 x 3} \) + \( \frac{4 x 1}{12 x 1} \)

\( \frac{6}{12} \) + \( \frac{4}{12} \)

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

\( \frac{6 + 4}{12} \) = \( \frac{10}{12} \) = \(\frac{5}{6}\)

46% of the water consumption is industrial use and 30% is personal use so (46% - 30%) = 16% more water is used for industrial purposes. 25,000 gallons are consumed daily so industry consumes \( \frac{16}{100} \) x 25,000 gallons = 4,000 gallons.

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

\( \frac{2}{7} \) x \( \frac{3}{5} \) = \( \frac{2 x 3}{7 x 5} \) = \( \frac{6}{35} \) = \(\frac{6}{35}\)

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

4\( \sqrt{45} \) + 2\( \sqrt{5} \)
4\( \sqrt{9 \times 5} \) + 2\( \sqrt{5} \)
4\( \sqrt{3^2 \times 5} \) + 2\( \sqrt{5} \)
(4)(3)\( \sqrt{5} \) + 2\( \sqrt{5} \)
12\( \sqrt{5} \) + 2\( \sqrt{5} \)

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