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
Add the numbers in each category and multiply that by the meal price. Then get the grand total.
6.5g + 12.5a + 9f + 6.5(11k) = ?
(As an aside, in terms of the cost for purchasing the food, how do you get to eat free? Also I really think might be better to calculate a higher cost for the teens, since they eat so much more than most adults, especially the guys.)
im trying to get the answer myself
To calculate the total number of guests at the party, you will need to count the number of each type of guest and sum them up.
Let's break down the guest list and assign variables to each group:
1. Grandparents: four grandparents (g = 4)
2. Adults: your parents, your best friend’s parents, your aunt and uncle, and your two next-door neighbors (a = 1 (your parents) + 1 (your best friend's parents) + 1 (your aunt and uncle) + 2 (your two next-door neighbors) = 5)
3. Friends: 17 guys (f = 17) and 16 girls (f = 16)
4. Kids under 11: your little brother and sister, each with three friends (k = 2 (your little brother and sister) + 2 * 3 (three friends each) = 8)
To represent all the guests using an algebraic expression, we can use the variables defined above:
Total Guests = g + a + f + k
Simplifying the expression:
Total Guests = 4 + 5 + (17 + 16) + 8
Total Guests = 4 + 5 + 33 + 8
Total Guests = 50 guests
Now, let's calculate the cost of feeding everyone at the party:
Using the given rates:
- Adults cost $12.50
- Senior Citizens and Children under 11 cost $6.50
- Teenagers cost $9.00
To calculate the total cost, we need to multiply the number of guests in each category by their respective cost and sum them up:
Total Cost = (Number of Adults * Cost per Adult) + (Number of Senior Citizens and Children under 11 * Cost per Senior Citizen or Child) + (Number of Teenagers * Cost per Teenager)
Plugging in the values:
Total Cost = (a * 12.50) + (g * 6.50) + (k * 6.50) + (f * 9.00)
Substituting the values we have:
Total Cost = (5 * 12.50) + (4 * 6.50) + (8 * 6.50) + ((17 + 16) * 9.00)
Calculating the expression:
Total Cost = 62.50 + 26.00 + 52.00 + 306.00
Total Cost = $446.50
Therefore, the cost of food for everyone at the party would be $446.50.