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. 39 large cakes are needed for the party so \( \frac{39}{9} \) = 4\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 18 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 18 x 3 = 54 small cakes during that time. 410 small cakes are needed for the party so \( \frac{410}{54} \) = 7\(\frac{16}{27}\) 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 5 + 8 = 13 cooks.

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 30mph \times 1h \)
30 miles

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

5\( \sqrt{12} \) - 5\( \sqrt{3} \)
5\( \sqrt{4 \times 3} \) - 5\( \sqrt{3} \)
5\( \sqrt{2^2 \times 3} \) - 5\( \sqrt{3} \)
(5)(2)\( \sqrt{3} \) - 5\( \sqrt{3} \)
10\( \sqrt{3} \) - 5\( \sqrt{3} \)

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

The amount of flour you need is (3\(\frac{1}{8}\) - 1\(\frac{5}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{25}{8} \) - \( \frac{13}{8} \)) cups
\( \frac{12}{8} \) cups
1\(\frac{1}{2}\) cups

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