Question

Judy took 30$ with her to spend on popcorn and drinks for herself and her friends at the movie theater. The price for each bag of popcorn was 5$. The price

of each drink was half the price of a bag of popcorn.

(a) Sketch the graph that represents the situation. Use one axis to present the number of bags of popcorn and the other axis to represent the number of drinks.

(b) Explain your graph.

Answer 1

Answer: function is y = -x/2 + 6 a) Graph added b) Graph explained

Explanation:

Let y = bags of popcorn

Let x = number of drinks

Each bag of popcorn cost 5$

Each drink cost 5$/2

Judy took $30 to spend on popcorn and drinks

5y + 5x/2 = 30

5y = -5x/2 + 30

y = -5x/2·5 + 30/5

y = -x/2 + 6

This is the equation of a line.

a) The graph is added to this answer.

b) This graph represents the number of drinks on the x axis and the popcorn bags on the y axis. We can see that there are several points marked in red where there are whole solutions for the number of drinks and popcorn bags.

x = 0 ; y = 6 ↩ Judy spent $30 on 6 bags of popcorn and 0 drinks

x = 2 ; y = 5 ↩ Judy spent $30 on 5 bags of popcorn and 2 drinks

x = 4 ; y = 4 ↩ Judy spent $30 on 4 bags of popcorn and 4 drinks

x = 6 ; y = 3 ↩ Judy spent $30 on 3 bags of popcorn and 6 drinks

x = 8 ; y = 2 ↩ Judy spent $30 on 2 bags of popcorn and 8 drinks

x = 10 ; y = 1 ↩ Judy spent $30 on 1 bags of popcorn and 10 drinks

x = 12 ; y = 0 ↩ Judy spent $30 on 0 bags of popcorn and 12 drinks

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