Question

Josiah is taking his friends to the movies. Each ticket costs $10, and popcorn is $5 a bag. There is a $3 service fee for the entire purchase. He has $75. If he buys 4 tickets, how many bags of popcorn can he buy? If x = number of tickets and y = number of bags of popcorn, derive the inequality to be used to answer the problem.

Answer 1

Each ticket costs $10. He bought "x" tickets. Ticket cost = 10*x
Each bag of popcorn costs $5.
He bought "y" bags of popcorn.
Popcorn cost = 5*y Service fee: $3
Total cost = 10x + 5y + 3 <= $75 is the inequality.
10x + 5y <= 72
If x = 4,
then 40 + 5y <= 72
5y <= 32
y <= 6.4
So y = 6 bags of popcorn.

Answer 2

Josiah can buy 6 more popcorn bags. 

The solution is as follows:
10x + 5y + 3 ≤ 75

if x = 4, the inequality will look like this:
10(4) + 5y + 3 ≤ 75
43 +5y ≤ 75
5y ≤ 32
y ≤ 6.4 or 6

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