how many of each type of pie were sold?

Question

A new bakery in a small city sells banana chocolate pies for $6.99 and pecan pies for $10.99.  The total number of pies sold on a busy Friday was 36. If the amount collected for all the pies that day was $331.64, how many of each type of pie were sold?
 

Answer 1

This problem gives a system of equations.  If you read the problem, they give two types of information about the sale: price/money collected and total number sold.  If you write an equation for each you will get the system.

 

Let x = the number of banana chocolate pies and y = the number of pecan pies.

 

Remember, the money received for selling the pies is simply the number of pies multiplied by their price.

Therefore,

6.99x + 10.99y = 331.64

 

The total pies is just the sum of how many of each were sold. Therefore,

x + y = 36

 

The system would be:

 

6.99x + 10.99y = 331.64

x + y = 36

 

We can solve the second equation for y: y = 36 - x.  This allows us to substitute 36 - x  in for y in the top equation.

 

6.99x + 10.99(36 - x) = 331.64

6.99x + 395.64 - 10.99x = 331.64

-4x + 395.64 = 331.64

-4x = -64

x = 16

 

If x = 16, then y = 36 - 16 = 20.

 

Therefore, they sold 16 banana chocolate pies and 20 pecan pies.

Answer 2

C= CHOCOLATE PIES

P=PECAN PIES

 

C+P=36                                                       6.99C+10.99P=331.64

SOLVE FOR C                                                SUBSTITUTE:  6.99(36-P)+10.99=331.64

C=36-P                                                          SOLVE:          251.64-6.99P+10.99P=331.64

                                                                                           251.64+4P=331.64

                                                                    SUBTRACT 251.64 FROM BOTH SIDES

                                                                                           4P=80

                                                                                             P=20

SINCE P=20, THEN C=36-20=16

Banana chocolate pies=16

Pecan Pies=20