32% of the water consumption is industrial use and 11% is personal use so (32% - 11%) = 21% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{21}{100} \) x 35,000 gallons = 7,350 gallons.

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

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.

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 10 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 10 x 3 = 30 small cakes during that time. 290 small cakes are needed for the party so \( \frac{290}{30} \) = 9\(\frac{2}{3}\) 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 5 + 10 = 15 cooks.

The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 3 factors [1, 2, 4] making 4 the greatest factor 28 and 80 have in common.