Question

1. Tickets to a movie theatre cost $12 for adults and $9 for children. There were twice as many children as adults in a group. The group spent less than $100 for tickets. Which inequality can be used to show how many adults, a, were in the group?

A 3a < 100 B 30a < 100 С 21a < 100 D 33a < 100 2.

Answer 1

Breakdown:

1. Tickets for adults cost $12 each, and tickets for children cost $9 each.
2. There were twice as many children as adults in the group.

Let's say there were 'a' adults in the group. Since there were twice as many children, the number of children would be 2a.

Now, let's calculate the cost of tickets for the group:

Cost for adults = $12 * a
Cost for children = $9 * 2a

Total cost = $12a + $18a = $30a

The problem states that the group spent less than $100 for tickets, which we can write as an inequality:

Total cost < $100
$30a < $100

Now we need to solve for 'a' to find the maximum number of adults in the group:

a < $100 / $30
a < 10/3

Since the number of adults must be a whole number (you can't have a fraction of a person), we can round down and write:

a ≤ 3

This means there can be a maximum of 3 adults in the group. The correct inequality that represents this is:

3a < 100

So, the correct answer is option A: 3a < 100.