To calculate the number of guests at your party, you can add up the number of guests in each category listed in the question:
Number of grandparents (g): 4
Number of adults (a): 2 (your parents) + 2 (best friend's parents) + 2 (aunt and uncle) + 2 (next door neighbors) = 8
Number of friends (f): 17 (guys) + 16 (girls) = 33
Number of kids under 11 (k): 1 (your little brother) + 1 (your little sister) + 3 (friends of your brother) + 3 (friends of your sister) = 8
Now, we can write an algebraic expression to represent the total number of guests:
Total number of guests = g + a + f + k
= 4 + 8 + 33 + 8
= 53 guests
Next, we need to calculate the cost of food for each category of guests:
Number of adult guests = a = 8
Cost per adult = $12.50
Number of senior citizens and children under 11 = g + k = 4 + 8 = 12
Cost per senior citizen or child = $6.50
Number of teenage guests = f = 33
Cost per teenager = $9.00
Now, let’s calculate the total cost of food for everyone at the party:
Total cost of food = (Number of adult guests × Cost per adult) + (Number of senior citizens and children under 11 × Cost per senior citizen or child) + (Number of teenage guests × Cost per teenager)
= (8 × $12.50) + (12 × $6.50) + (33 × $9.00)
= $100 + $78 + $297
= $475
Therefore, the total cost to feed everybody at the party is $475.