Part 2: Now it’s time to make the guest list! Figure out how many guests you will have at your party, and how much it will cost to feed everybody.
You have four grandparents coming. For the adults, you have your parents, your best friend’s parents, your aunt and uncle, and your two next door neighbors that have known you forever. From school you have 17 guys coming and 16 girls (You get to eat free!). Your little brother and sister (under the age of 11) are coming too and they each invited three friends. Use the variables in the table to write and simplify an algebraic expression to represent all of your guests.
Grandparents g
Adults a
Your friends f
Kids under 11 k
With all this dancing, your guests will get hungry! Everyone at a party needs to eat… With the guest list above, calculate the cost of food for everyone at the party.
Adults cost $12.50
Senior Citizens and Children under 11 cost $6.50
Teenagers cost $9.00
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.