Question

The local radio station is giving away some tickets to the circus. Adult tickets cost the station $8 each while children's tickets cost $6. The station wants to spend no more than $172. Let x = the number of adult tickets and y = the number of children's tickets. Show all possible solutions by graphing a linear inequality.

Answer 1

The graph in the attached figure

Explanation:

Let

x------> the number of adult tickets

y-----> the number of children's tickets

we know that

`8x+6y\leq 172` -----> linear inequality that represent the situation

using a graphing tool

The solution is the triangular shaded area between the values of x and y positives

see the attached figure

Answer 2

"no more than" implies a "less than or equal to" inequality, meaning we use this sign: ≤

x= number of adult tickets, which are $8 each
y= number of children's tickets, which are $6 each
Therefore:
8x + 6y ≤ 172