The amount of flour you need is (2\(\frac{3}{8}\) - \(\frac{1}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{19}{8} \) - \( \frac{2}{8} \)) cups
\( \frac{17}{8} \) cups
2\(\frac{1}{8}\) cups

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 18 meters so the equation becomes: 2w + 2h = 18.

Putting these two equations together and solving for width (w):

2w + 2h = 18
w + h = \( \frac{18}{2} \)
w + h = 9
w = 9 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 9 - 2w
3w = 9
w = \( \frac{9}{3} \)
w = 3

Since h = 2w that makes h = (2 x 3) = 6 and the area = h x w = 3 x 6 = 18 m²

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. 39 large cakes are needed for the party so \( \frac{39}{12} \) = 3\(\frac{1}{4}\) 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 3 hours, a single cook can bake 15 x 3 = 45 small cakes during that time. 430 small cakes are needed for the party so \( \frac{430}{45} \) = 9\(\frac{5}{9}\) 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 + 10 = 14 cooks.

50% of the water consumption is industrial use and 23% is personal use so (50% - 23%) = 27% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{27}{100} \) x 35,000 gallons = 9,450 gallons.

The factors of 16 are [1, 2, 4, 8, 16] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 the greatest factor 16 and 76 have in common.