If a single cook can bake 4 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 4 x 3 = 12 large cakes during that time. 37 large cakes are needed for the party so \( \frac{37}{12} \) = 3\(\frac{1}{12}\) 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. 480 small cakes are needed for the party so \( \frac{480}{54} \) = 8\(\frac{8}{9}\) 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 + 9 = 13 cooks.

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

7\( \sqrt{125} \) - 7\( \sqrt{5} \)
7\( \sqrt{25 \times 5} \) - 7\( \sqrt{5} \)
7\( \sqrt{5^2 \times 5} \) - 7\( \sqrt{5} \)
(7)(5)\( \sqrt{5} \) - 7\( \sqrt{5} \)
35\( \sqrt{5} \) - 7\( \sqrt{5} \)

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

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

9\( \sqrt{2} \) x 5\( \sqrt{2} \)
(9 x 5)\( \sqrt{2 \times 2} \)
45\( \sqrt{4} \)

Now we need to simplify the radical:

45\( \sqrt{4} \)
45\( \sqrt{2^2} \)
(45)(2)
90

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.

The greatest common factor (GCF) is the greatest factor that divides two integers.