My actual question is in the description

Question

A local buffet charges $6.50 per person for the basic buffet and $9.00 for the deluxe buffet. If there are 28 people eating and the total cost was $222.00 before tax, how many got the basic and how many got the deluxe.  

Answer 1

First, read and re-read the problem until you understand it and can put it into your own words.  How's this:  "28 people are either the $6.50 buffer or the $9.00 deluxe buffet for a total of $222.00 before tax.  How many ate each?"

 

Define variables (if possible, define what the problem asks you to find).  Let:

    B = number of people eating basic buffet

    D = number of people eating deluxe buffer

 

Extra info:  (cost of meal)*(number of meals) = cost                    [meals cancel out]

 

Translate:

  "28 people eating"    means     B + D = 28

  "$6.50 per person for the basic buffet and $9.00 for the deluxe buffet...total cost was $222.00"   means

        $6.50B + $9.00D = $222.00

 

O.K., now the easy math:

   Let's substitute:     From the first equation, we know B = 28-D, so:

             $6.50B + $9.00D = $222.00

              65B + 90D = 2220              (multiply by 10; divide by $; I have trouble with decimals)

             65(28-D) + 90D = 2220

            1820 - 65D + 90D = 2220              [distribute]

                    25D = 400                      

                      D = 16

And, B + (16) = 28, so

           B = 12

 

Checking (very important):

  Is  $6.50(12) + $9.00(16) = $222.00   ?

          $78.00 +  $144.00 = $222.00   ?

                   $222.00 = $222.00   ? yes

Answer 2

You have two variables, lets call them X and Y, for the basic and the deluxe, respectively. We also have two equations.

 

6.50X + 9.00Y = 222.00

 

X + Y = 28 -- > The total number of people eating.

 

Y = 28 - X

 

Plug into first equation.

 

6.5X + 9(28-X) = 222 -->    6.5x + 252 - 9X = 222

6.5X - 9X = 222-252

-2.5X = -30

 

X=12 --> Basic Buffet

 

Y = 28 - X = 28 - 12 = 16 --> Deluxe Buffet