Answer:
1. The total cost of movie and the total cost of refreshments purchased and the total cost of video games played cannot exceed 40
2. 14.50 + 7.75x + 0.75y ≤ 40
3. y ≤ 34 - 10.333x
4. See attached graph
5.
one refreshment means you can play 23 times
two refreshments means you can play 13 times
three refreshments means you can play 3 times
Step-by-step explanation
We have to assume that you can see one movie but but buy multiple refreshments and play multiple video games. A refreshment is considered to be one drink and one popcorn.
If not we have a situation where we have three unknowns and it will be difficult to solve in a 2D context
1. Verbal inequality model
The total cost of one movie and the total cost of refreshments purchased and the total cost of video games played cannot exceed 40
2. Algebraic Inequality Model
Since the cost of a movie is 14.50 and you are seeing only 1 movie, the cost is 14.50(1) = 14.50
Assume you are going to buy x refreshments. Total cost of refreshments = 7.75x
Assume you are going to play y video games. Total cost of video games played = 0.75y
This cannot be greater than 40 i.e ≤ 40
So the algebraic inequality is
14.50 + 7.75x + 0.75y ≤ 40
3. Solving the inequality
Subtracting 14.50 from both sides we get
7.75x + 0.75y ≤ 25.50
Subtracting 14.50 from both sides we get
7.75x + 0.75y ≤ 25.50
Subtract 7.75x from both sides:
0.75y ≤ 25.50- 7.75x
Divide both sides by 0.75
y ≤ 25.50/0.75 - 7.75x/0.75
which is
y ≤ 34 - 10.333x
3. Graph of Inequality
This is an inequality in 2 variables and can be graphed.
See attached graph. The shaded portion represents the inequality
y ≤ 34 - 10.333x
Note that since neither x nor y can be < 0, we should not consider any portion of the shaded area which would mean two more constraints x ≥ 0 and y ≥ 0 but in this case I have stuck to only the above one inequality
5. Possible number of times you can play the same video game
Again we consider only 1 movie and multiple refreshments and video games
Using the inequality y ≤ 34 - 10.33x
If x = 1 refreshment,
y ≤ 34 - 10.33 x 1
y ≤ 23.67 or max 23 times you can play the video game max
If x = 2,
y ≤ 34 - 10.33 x 2
y ≤ 13.34 or maximum 13 times
If x = 3
y ≤ 34 - 30.99
y ≤ 3.01 or maximum 3 times
