If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 32 large cakes are needed for the party so \( \frac{32}{9} \) = 3\(\frac{5}{9}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 17 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 17 x 3 = 51 small cakes during that time. 150 small cakes are needed for the party so \( \frac{150}{51} \) = 2\(\frac{16}{17}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 4 + 3 = 7 cooks.

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

6\( \sqrt{27} \) - 2\( \sqrt{3} \)
6\( \sqrt{9 \times 3} \) - 2\( \sqrt{3} \)
6\( \sqrt{3^2 \times 3} \) - 2\( \sqrt{3} \)
(6)(3)\( \sqrt{3} \) - 2\( \sqrt{3} \)
18\( \sqrt{3} \) - 2\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them:

To multiply terms with radicals, multiply the coefficients and radicands separately:

6\( \sqrt{2} \) x 7\( \sqrt{8} \)
(6 x 7)\( \sqrt{2 \times 8} \)
42\( \sqrt{16} \)

Now we need to simplify the radical:

42\( \sqrt{16} \)
42\( \sqrt{4^2} \)
(42)(4)
168

To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{7} \) ÷ \( \frac{1}{8} \) = \( \frac{3}{7} \) x \( \frac{8}{1} \)

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

\( \frac{3}{7} \) x \( \frac{8}{1} \) = \( \frac{3 x 8}{7 x 1} \) = \( \frac{24}{7} \) = 3\(\frac{3}{7}\)

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{210mi}{30mph} \)
7 hours