Final answer:
To find the equation the Mexican food restaurant uses for catering costs, we analyze the increase in cost per additional guest and determine the fixed setup and cleanup fee. The consistent increase of $7 per additional guest and the fixed fee of $25 established with 20 guests lead us to the equation C = 7g + 25.
Step-by-step explanation:
The question is asking to determine the equation a Mexican food restaurant uses to calculate the total cost for catering a party with 20 or more guests based on a table of values provided. To solve this, we will first analyze the costs given for different numbers of guests to find the pattern. Then we will match this pattern to one of the given equations.
Looking at the costs given, when 20 guests are catered, the cost is $165, and when 25 guests are catered, the cost is $200. The difference here is 5 guests and the cost increases by $35, which suggests that each additional guest adds $7 to the total cost ($35/5 guests = $7/guest). To double-check this, when the number of guests increases from 25 to 40 (an increase of 15 guests), the total cost increases from $200 to $305. Calculating the cost per guest, we get ($305 - $200) / (40 guests - 25 guests) = $105 / 15 guests = $7/guest. This confirms the cost per guest is consistent.
Since the cost increases by $7 for each additional guest, we start with the cost for 20 guests, which is $165, as the fixed setup and cleanup fee (as no cost is provided for fewer than 20 guests, we consider 20 guests to be the base number). Now, we need an equation in the form of C = constant + 7g, where C is the total cost and g is the number of guests minus 20 (since the equation needs to apply starting from 20 guests). So, we subtract the cost of 20 guests (20 × $7 = $140) from $165 to get the setup fee: $165 - $140 = $25.
Therefore, the equation used by the Mexican food restaurant is C = 7g + 25.