Question

PLEASE HELP!

At a local fair, the admission fees are $1.50 for children, $3 for college students, and $5 for adults.


On Saturday, 1500 tickets were sold and brought in $5500.

The number of college student tickets sold was 100 less than the number of children's tickets sold.

How many children's tickets were sold?

Answer 1

Children's' Tickets Sold: 400

College Tickets Sold: 300

Adult Tickets Sold: 800

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Pre-Calculus

• Matrices
• Reduced Row Echelon Form (RREF)

Explanation:

Step 1: Define Variables

x = children tickets

y = college tickets

z = adult tickets

Step 2: Define Systems

Use the given information to set up the equations.

x + y + z = 1500

1.5x + 3y + 5z = 5500

y = x - 100

Step 3: Redefine Systems

x + y + z = 1500

1.5x + 3y + 5z = 5500

-x + y = -100

Step 4: Solve for x

1. Rewrite [Matrix]:
   `\left[\begin{array}{ccc}1&1&1 | 1500\\1.5&3&5 | 5500\\-1&1&0 | -100\end{array}\right]`
2. [Matrix] RREF:
   `\left[\begin{array}{ccc}1&0&0 | 400\\0&1&0 | 300\\0&0&1 | 800\end{array}\right]`

Here we see that our x = 400, y = 300, and z = 800. Correspond this with our defined variables and we have our answer.