Question

A group of 7 people spent $33.50 on movie tickets. They paid $6.50 for each adult ticket and $3.50 for each child's ticket. We would like to determine how many of each type of ticket was purchased. A. Specifically define variables for this system B. Write a system of equations that reflects the relationships described in this situation

Answer 1

Number of Adult tickets = 3

Number of student tickets = 4

Explanation:

Let the number of Adults tickets = x

The number of students tickets = y

A. Specifically define variables for this system

x + y = 7...... Equation 1

They paid $6.50 for each adult ticket and $3.50 for each child's ticket.

$6.50 × x + $3.50 × y = $33.50

6.50x + 3.50y = 33.50.......Equation 2

B. Write a system of equations that reflects the relationships described in this situation

x + y = 7...... Equation 1

x = 7 - y

6.50x + 3.50y = 33.50.......Equation 2

6.50(7 - y) + 3.50y = 33.50

45.5 - 6.5y + 3.5y = 33.5

45.5 - 33.5 = 6.5y -3.5y

12 = 3y

y = 12/3

y = 4 tickets

x + y = 7...... Equation 1

x + 4 = 7

x = 7- 4

x = 3 tickets