Question

Larry can spend at most $2800 to renovate his home. One roll of wallpaper costs $35, and one can of paint costs $40. He needs at least 20 rolls of wallpaper and at least 30 cans of paint. Identify the graph that shows all possible combinations of wallpaper and paint that he can buy. Also, identify two possible combinations.Possible combinations: (10, 10), (20, 15)Possible combinations: (25, 35), (40, 30)Possible combinations: (50, 40), (10, 60)Possible combinations: (11, 25), (18, 15)

Answer 1

`(25,35)`

1) The best way to tackle this question is to set the inequalities then plot, and then we can check.

2) Gathering the data we can write out the following inequalities:

`\begin{gathered} 35w+40c\leq2800 \\ w\ge20 \\ c\ge30 \end{gathered}`

Notice that "w" stands for rolls of wallpaper and "c" cans of paint.

3) Let' plot them and in the darker region we'll see where are the possible solutions, i.e. combinations:

Note that this yellow part is the area where are located those possible solutions.

Let's plot the options to check them within the graph:

Note that among the options the only one that is located in the darkest region is the (25, 35)