Question

Mr. Ramirez purchased 32 concert tickets for a total of $360. The concert tickets

cost $15 for adults and $10 for children under the age of 12.
• 1 point: Write and solve a system of equations to represent the given
scenario.
• 2 points: Interpret the solution.

Answer 1

Solution: x=8, y=24

Part 2. Mr. Ramirez purchased 8 adult tickets and 24 children tickets

Explanation:

System of Equations

The concert tickets cost for adults is $15 and $10 for children.

Let's call

x = number of adults tickets purchased

y = number of children tickets purchased

Mr. Ramirez purchased 32 tickets, thus:

x + y = 32

The total cost of the 32 tickets is $360:

15x + 10y = 360

* Part 1. The system of equations is:

x + y = 32 [1]

15x + 10y = 360 [2]

Solving [1] for x:

x = 32 - y [3]

Substituting in [2]:

15(32 - y) + 10y = 360

Operating:

480 - 15y + 10y = 360

-5y = 360 - 480

-5y = -120

Dividing by -5

y = 24

Substituting in [3]

x = 32 - 24 = 8

Solution: x=8, y=24

Part 2. Mr. Ramirez purchased 8 adult tickets and 24 children tickets