Question

Alyssa’s family went to the movies with Andrea’s family. They each bought their own tickets. Alyssa bought 1 adult and 2 child tickets for $16. Andrea spent $28 on 2 adult tickets and 3 child tickets. Which system of equations best represents the situation where a is adult and c is child?

a. a + 2c = 16, 2a + 3c = 28
b. 2a + c = 16, 3a + 2c = 28
c. 2a + 2c = 16, 3a + 3c = 28
d. a + c = 16, 2a + 3c = 28

Answer 1

The system of equations that represents the situation of Alyssa and Andrea buying movie tickets is a + 2c = 16, 2a + 3c = 28. 'a' stands for the adult ticket price, and 'c' for the child ticket price.

Step-by-step explanation:

Alyssa’s family and Andrea’s family buying movie tickets give us two scenarios which can be represented as a system of linear equations. Let 'a' be the cost of an adult ticket and 'c' be the cost of a child ticket. From the information given:

• Alyssa bought 1 adult ticket and 2 child tickets for $16: a + 2c = 16.
• Andrea spent $28 on 2 adult tickets and 3 child tickets: 2a + 3c = 28.

This system of equations accurately represents the given situation, and thus the correct answer is option a: a + 2c = 16, 2a + 3c = 28.