Answer:
7
Explanation:
We can solve this problem by making an equation for the monthly bill. First, the cost is $59.99 per month, and that cannot be decreased, so we must add all costs to that amount. Next, it costs $5.49 per first run movie, so for each first run movie, we add $5.49 to the total. Therefore, we can write our equation as
59.99 + 5.49 per first run movie = monthly bill
Representing the number of first run movies as r, we can say
59.99 + 5.49 * r = monthly bill
Next, the monthly bill should be less than or equal to 100, so we can say
monthly bill ≤ 100
59.99 + 5.49 * r = monthly bill ≤ 100
Moreover, we want to maximize r, or the amount of first run movies. Because we add money to the monthly bill for each movie, to maximize r, we have to find the maximum money we can spend on the monthly bill that is still less than or equal to 100. To do this, we set the monthly bill to its maximum limit, or 100, so we have
59.99 + 5.49 * r = 100
subtract 59.99 from both sides to isolate the f and its coefficient
40.01 = 5.49 * r
divide both sides by 5.49 to isolate the variable
r ≈ 7.29
Since we can't buy .29 of a movie, and rounding up to 8 movies would cause us to go past 100 dollars, the maximum movies he can watch if he wants to keep his monthly bill ≤ 100 is 7