Question

Judy took $45 with her to spend on popcorn and drinks for herself and friends at the movie theater. The price for each bag of popcorn was $5 and the price for each drink was $3. This can be represented by the equation 5x+3y=45 where x represents the number of bags of popcorn and y represents the number of drinks (this assumes she will spend all $45). a) Find the x and y intercepts of the equation. Show how you found the x-intercepts in the "Show Your Work" section below, then write your answers here: x-intercept: y-intercept: b) Use your intercepts to sketch the graph in the "Show Your Work" section below. c) Use your graph to find another combination of popcorn and drinks she can purchase for $45. She can purchase bags of popcorn and drinks for $45. RUBRIC:

Answer 1

The relationship between the number of popcorn and drinks is linear relationship
The responses are;
(a) Please find attached the required graph created with MS Excel
(b) From the graph, we have that as the number of bags of popcorn Judy buys increases, the number of drinks decreases linearly
Reasons:
The given parameter are;
Amount Judy took with her to spend on popcorn and drinks = $30
Price of each bag of popcorn = $5
Price of each drink = Half the price of a bag of popcorn
∴ The price of each drink = (\$ 5 )/(2) = \$ 2.5
(a) Let X represent the number of bags of popcorn Judy buys and let Y represent the number of drinks she buys, we have;
5·X + 2.5·Y = 30
2.5·Y = 30 - 5·X
Which gives;
Y = (30 - 5\cdot X)/(2.5) = 12 - 2 \cdot X
Y = 12 - 2·X
Using the above equation, the graph of popcorn and drinks bought by
Judy is plotted with MS Excel and attached here
(b) The data in the graph are presented as follows
\begin{array} \mathbf{Bags \ of \ Popcorn}&&\mathbf{Drinks}\\0&&12\\1&&10\\2&&8\\3&&6\\4&&4\\5&&2 \\6&&0\end{array}\right]
The point corresponding to the y-intercept is the point that gives the
maximum number of drinks Judy can buy if she does not buy popcorn is
12 drinks. The number of drinks she can buy reduces by 2 for each bag of
popcorn she buys, such that she can buy 6 bags of popcorn and no drinks
which is the x-intercept.