problem solving

Question

The Concordia theater contains 500 seats, and the ticket prices for a recent play were $43 for adults and $28 for children. For one sold out matine, if the total proceeds were $16,805 how many of each tups of ticket were sold? 

Answer 1

Let A be the number of Adult Tickets

Let C be the number of Child Tickets

 

F1)  A + C = 500

F2)  43A + 28C = 16805

 

A = 500 - C  (from F1, solving for A)

Plug this new A into F2

 

43 * (500 - C) + 28C = 16805

Solve for C:

21500 - 43C + 28C = 16805

21500 - 16805 = 43C - 28C

4695 = 15C

C = 4695/15 = 313

 

Plug C back into F1

A + 313 = 500

A = 500 - 313

A = 187

 

Plug A and C back into F2 to check your answer:

43(187) + 28(313) = 16805

8041 + 8764 = 16805

16805 = 16805 !!!!!

 

Answer 2

This is a two equations and two unknowns problem.

 

If x=adults, and y=children then

 

adults+children=total seats 

or

x+y=500

 

and

43x+28y=16,805

 

I would solve by elimination, so multiply the first equation by 28

28 x+28 y=14,000

and

subtract

15 x=2,805

and divide by sides by 15

x=187

 

plug back into the simpler of the two equations

187+y=500

y=313

 

I hope this helps,

 

David E.