Jamie will choose between two catering companies for an upcoming party. Company A charges a set-up fee of $500 plus $25 for each guest. Company B charges a set-up fee of $200 plus $30 per guest.
a. Write expressions that you can use to determine the amount each company charges for g guest.
b. Jamie learns that the $500 set-up fee for Company A includes payment for 20 guests. The $25 guest charge is for every guest over the first 20. If there will be 50 guests which company will cost the least?
solve for g
500+25g = 200+30g
for the rest, ....
"guest charge is for every guest over the first 20" ----> (g-20)
make use of that hint
a. The expressions to determine the amount each company charges for g guests are:
- For Company A: $500 + $25g
- For Company B: $200 + $30g
b. Let's calculate the cost for each company given that there will be 50 guests:
- For Company A: The set-up fee is $500, and since it already includes payment for 20 guests, we need to calculate the remaining guests, which is 50 - 20 = 30. So, the additional cost for the remaining 30 guests is $25 * 30 = $750. Therefore, the total cost for Company A would be $500 + $750 = $1250.
- For Company B: The set-up fee is $200, and the cost per guest is $30, so the total cost for 50 guests would be $200 + ($30 * 50) = $200 + $1500 = $1700.
From the calculations, we can see that Company A will cost $1250 and Company B will cost $1700. Therefore, Company A will cost the least.
a. The expression to determine the amount Company A charges for g guests is: 500 + 25g.
The expression to determine the amount Company B charges for g guests is: 200 + 30g.
b. For Company A, there is a set-up fee of $500, which includes payment for 20 guests. For each additional guest, the charge is $25 per guest. So for 50 guests, the amount charged by Company A would be: 500 + 25(50-20) = 500 + 25(30) = 500 + 750 = $1250.
For Company B, there is a set-up fee of $200 and a charge of $30 per guest. So for 50 guests, the amount charged by Company B would be: 200 + 30(50) = 200 + 1500 = $1700.
Therefore, Company A will cost the least for 50 guests, with a charge of $1250.
a. To determine the amount each company charges for g guests, we can use the following expressions:
- For Company A: $500 + $25g
The set-up fee is a fixed amount of $500, and for each guest after the initial 20, there is an additional charge of $25.
- For Company B: $200 + $30g
The set-up fee is a fixed amount of $200, and for each guest, there is an additional charge of $30.
b. If there will be 50 guests, we can calculate the total cost for each company using the expressions from part a:
- For Company A: $500 + $25 * (50 - 20) = $500 + $25 * 30 = $500 + $750 = $1250
The additional charge is $25 per guest over the first 20 (50 - 20 = 30), so the total cost for Company A is $1250.
- For Company B: $200 + $30 * 50 = $200 + $1500 = $1700
For Company B, there is no initial set-up fee for a certain number of guests, so the total cost is $1700 for 50 guests.
Comparing the two companies, we find that if there will be 50 guests, Company A will cost the least, with a total cost of $1250, while Company B will cost $1700.