Solving a System of Linear Equations in a Real-World Scenario

This video tutorial demonstrates how to solve an application problem using a system of linear equations. The problem involves determining the number of adult and children's tickets sold at a theater, given the total number of seats and total sales. The tutorial guides viewers through setting up equations for the total tickets and sales, solving the system using substitution, and verifying the solution. The final answer reveals the number of adults and children in the theater.

What is the cost of an adult movie ticket in the given problem?

• $7.00

• $5.50

• $10.00

• $12.00

How many seats are there in the theater?

• 250

• 200

• 150

• 218

What equation represents the total number of tickets sold?

• a + c = 218

• a + c = 1463

• a - c = 1463

• a - c = 218

What is the cost of a children's movie ticket?

• $4.00

• $6.00

• $5.50

• $7.00

What equation represents the total amount of money collected?

• 7a + 5.5c = 1463

• 5.5a + 7c = 218

• 7a + 5.5c = 218

• 5.5a + 7c = 1463

What method is used to solve the system of equations?

• Matrix

• Substitution

• Elimination

• Graphing

After substitution, what is the equation used to find the number of children's tickets?

• 5.5a + 7(218 - a) = 1463

• 7(218 - c) + 5.5c = 1463

• 7c + 5.5(218 - c) = 1463

• 7a + 5.5(218 - a) = 1463

How many children's tickets were sold?

• 176

• 100

• 76

• 42

How many adult tickets were sold?

• 42

• 76

• 100

• 176

What is the final conclusion about the number of adults and children in the theater?

• 100 adults and 118 children

• 42 adults and 176 children

• 176 adults and 42 children

• 118 adults and 100 children