The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

If a single cook can bake 2 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 2 x 4 = 8 large cakes during that time. 35 large cakes are needed for the party so \( \frac{35}{8} \) = 4\(\frac{3}{8}\) 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 4 hours, a single cook can bake 18 x 4 = 72 small cakes during that time. 310 small cakes are needed for the party so \( \frac{310}{72} \) = 4\(\frac{11}{36}\) 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 + 5 = 10 cooks.

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

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{220mi}{55mph} \)
4 hours

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 40% the radius (and, consequently, the total area) increases by \( \frac{40\text{%}}{2} \) = 20%

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.