Final answer:
To find the number of guests for which the cost of Caterer A is the same as Caterer B, set up an equation and solve for the variable. The cost for Caterer A will be the same as Caterer B when there are 0 guests. For 36 guests, the cost for Caterer A would be $360.
Step-by-step explanation:
To find the number of guests for which the cost of Caterer A is the same as Caterer B, we need to set up an equation and solve for the variable. Let's assume the cost for Caterer A is represented by the function A(g) and the cost for Caterer B is represented by the function B(g), where 'g' represents the number of guests. We can set up the equation A(g) = B(g) and solve for 'g'.
For example, if Caterer A charges $10 per guest and Caterer B charges $25 per guest, the equation would be 10g = 25g. Simplifying the equation, we get 10g - 25g = 0, which gives us -15g = 0. Dividing both sides of the equation by -15, we find that g = 0. Therefore, the cost of Caterer A would be the same as Caterer B when there are 0 guests.
To find the cost for 36 guests, we can substitute the value of 'g' into either A(g) or B(g) function. Let's say Caterer A charges $10 per guest, then the cost for 36 guests would be A(36) = 10 * 36 = $360.