First, solve for \( \left|z - 6\right| \):

\( \left|z - 6\right| \) - 1 = 4
\( \left|z - 6\right| \) = 4 + 1
\( \left|z - 6\right| \) = 5

The value inside the absolute value brackets can be either positive or negative so (z - 6) must equal + 5 or -5 for \( \left|z - 6\right| \) to equal 5:

So, z = 1 or z = 11.

The factors of a number are all positive integers that divide evenly into the number. The factors of 28 are 1, 2, 4, 7, 14, 28.

1

If a single cook can bake 4 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 4 x 2 = 8 large cakes during that time. 24 large cakes are needed for the party so \( \frac{24}{8} \) = 3 cooks are needed to bake the required number of large cakes.

If a single cook can bake 15 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 15 x 2 = 30 small cakes during that time. 320 small cakes are needed for the party so \( \frac{320}{30} \) = 10\(\frac{2}{3}\) 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 3 + 11 = 14 cooks.

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.