Linear Systems application

Question

A movie theater charges $ 9 for adults and $ 6 for seniors. On a particular day when 330 people paid an admission, the total receipts were $ 2566. Round your answers to the nearest integers.

 

 

How many who paid were adults?

 

 

How many who paid were seniors?

Answer 1

 

Are the prices in the correct order?

Are you sure the 330 and the 2566 are correct?

 

A + S = 330 --> S = 330 - A

 

9A + 6S = 2566

 

9A + 6(330-A) = 2566

 

9A + 1980 - 6A = 2566

 

3A + 1980 = 2566

 

3A = 2566 - 1980

 

3A = 586

 

A = 586/3 = 195.333... = 195 and 1/3

 

S = 134.66... = 134 and 2/3

 

The answer checks:   (195 and 1/3)*9 + (134 and 2/3) * 6 =

                                    586/3*9   + 404/3*6 =

 

                                 1758 + 808 = 2566

                             

 

195 adults and 135 seniors is $1 off