Question

Barbara is deciding between Banquet Chefs and CeCe's Catering to cateran awards banquet. Banquet Chefs charges $28/guest plus $590 servicefee. Cece's Catering charges $31/guest plus $425 service fee. Barbaraneeds to choose the company that costs less. Who should she choose if20 guests are attending?

Answer 1

Banquet chefs charge $28 per guest.

This means if:

there is 1 guest, they charge $28

there are 2 guests, they charge $28 x 2 = $56

there are 3 guests, they charge $28 x 3 = $84

there are 4 guests, they charge $28 x 4 = $112

Thus, we can generalize that if they have n guests,

they charge $28 x n = $28n

In addition to this charge per each guest, Banquet Chefs charge $590 for service fee.

Thus, if Barbara is to choose Banquet chefs, the fees she ought to pay is given by:

`Fee=28n+590`

If she goes for Cece's catering, she has to pay $31 for each guest.

This means that if:

there is 1 guest, they charge $31

there are 2 guests, they charge $31 x 2 = $62

there are 3 guests, they charge $31 x 3 = $93

Thus, we can generalize that if Barbara invites n guests then she has to pay:

$31 x n = $31n

However, the question also says Cece's catering charges extra $425 for service fee.

Therefore, the total amount Barbara would pay is modelled by the equation:

`Fee=31n+425`

Now, the question says that 20 guests attended the event. This means n = 20

To know how much Barbara has to pay for either Banquet chefs or Cece's catering, we simply substitute n= 20 into both equations respectively then pick the one with the lower fees.

This is done below:

Banquet Chefs:

`\begin{gathered} \text{Fee}=28n+590 \\ n=20 \\ Fee=28*20+590 \\ \therefore Fee=1150 \end{gathered}`

For Banquet chefs, Barbara would pay $1150 for 20 guests.

Now, let us calculate for Cece's catering.

Cece's catering:

`\begin{gathered} Fee=31n+425 \\ n=20 \\ Fee=31*20+425 \\ \\ \therefore Fee=1045 \end{gathered}`

For Cece's catering, Barbara would pay $1045 for 20 guests.

Therefore, Barbara should choose Cece's catering because they charge $1045 for 20 guests which is lower than Banquet chefs who charge $1150