what is the solution ?

Question

To raise funds, a school sells two kinds of raffle tickets. Deluxe tickets sold for $6.00, while regular tickets sold for $1.50. There were 371 tickets sold for a total of $822. Proceeds from this raffle purchased software for the computer lab. How many tickets of each kind were sold?

Answer 1

Let d: Deluxe tickets

Let r: Regular tickets

Set the system of equations:

6d + 1.5r = 822

d + r = 371

Isolate d:

d = 371 - r

Replace d in the first equation:

6 (371 - r) + 1.5r = 822

2226 - 6r + 1.5r = 822

-4.5r = 822 - 2226

-4.5r = -1404

r = -1404 / -4.5

r = 312

Replace r in the second equation:

d + 312 = 371

d = 371 - 312

d = 59

They sold 312 regular tickets and 59 deluxe tickets.

Answer 2

Step 1: Set up your equations

1. Assuming x = regular and y = deluxe

x + y = 371

1.5x + 6y = 822

Step 2; Solve using any method of systems of equations:

There are 4 common methods for systems of equations

1. Substitution
2. Elimination
3. Graphing
4. Matrices

I'm good with my calculator so I'm going to use 4. Matrices and setup a 2x3 matrix. Then I'll use rref() to calculate the answers. Please note any of these methods will get you the correct answer if you set up your equations properly.

x = 312 (regular tickets were sold)

y = 59 (deluxe tickets were sold)