Final answer:
The equation relating the number of apples (a) to the number of pies (p) is a = 4.5p, where 4.5 represents the number of apples needed per pie, based on the proportion of 9 apples for 2 pies.
Step-by-step explanation:
The question asks to write an equation that relates the number of apples (a) to the number of pies (p) given that 9 apples are needed to make 2 pies. To find this relation, you can use the concept of proportions or a ratio. Since 9 apples make 2 pies, we can express the number of apples as a multiple of the number of pies. The conversion factor here is 9 apples per 2 pies, or 4.5 apples per 1 pie.
Using this conversion factor, the equation that we can use, to relate a to p, is a = 4.5p. Therefore, each pie requires 4.5 apples. So, for any number of pies, we can multiply the number of pies (p) by 4.5 to find the number of apples (a) needed. The correct answer that represents this relationship is therefore option b) a = 4.5p.