Simple cost/capacity problem

[trmn8r]

You have begun your first week as purchasing agent for moes tavern. You have a beer budget of $540 to spend on canned and bottled beer. The storage room in the back of the tavern is 110 ft/cubed. Case of bottled beer costs $12 and has a volume of 2.5 feet, canned is $10 with a volume of 2 feet.
a)How much of each kind of beer should you buy if you want to spend your whole budget and use all remaining space?
b)Graph equations for capacity and cost and show intersection point on the graph. Be sure to label your graph and clearly show your scale.


I have created the formulas 540=12x +10y and 110=2.5x +2y

Using the first formula and trial and error, i find values for x and y, and by entering them into the second formula, I can see if they work. By doing so I have found that 20 Bottled and 30 Canned cases meets the space and cost requirements. I just totally forget how to proceed from here to part B. Its been about 11 years since I took math 11 and I am a little rusty, could it be that the method |I used is not the preferred method and there is an easier or more correct formula I could then graph? Taking a business assessment test tomorrow and this is the only question I had issue with, please help as I'm not sure how many of these graphing questions are going to be on said test. Thanks.

 

[stapel]

could it be that the method I used is not the preferred method

Since you are given information sufficient for exactly two variables (thus graphable) and exactly two equations (thus solveable as a system of equations), yes, you should probably use a standard method. (By the way, guess-n-check is never "preferred" on tests, etc, where time is of the essence.)

You have begun your first week as purchasing agent for moes tavern. You have a beer budget of $540 to spend on canned and bottled beer. The storage room in the back of the tavern is 110 ft/cubed. Case of bottled beer costs $12 and has a volume of 2.5 feet, canned is $10 with a volume of 2 feet.
a)How much of each kind of beer should you buy if you want to spend your whole budget and use all remaining space?
b)Graph equations for capacity and cost and show intersection point on the graph. Be sure to label your graph and clearly show your scale.

I have created the formulas 540=12x +10y and 110=2.5x +2y

I will guess that "x" represents "the number of cases of bottled beer", while "y" represents "the number of cases of canned beer".

Using the first formula and trial and error, i find values for x and y, and by entering them into the second formula, I can see if they work.

To learn how to solve systems of linear equations, try here. To learn how to solve linear equations for "y=", try here. To learn how to graph linear equations, try here.

Taking a business assessment test tomorrow and this is the only question I had issue with, please help as I'm not sure how many of these graphing questions are going to be on said test.

It is likely that there will be other algebra topics on this assessment, as they may be expected to be required in your course of study. You might want to consider taking algebra, and maybe statistics, before proceeding further.

 

[Ishuda]

You have begun your first week as purchasing agent for moes tavern. You have a beer budget of $540 to spend on canned and bottled beer. The storage room in the back of the tavern is 110 ft/cubed. Case of bottled beer costs $12 and has a volume of 2.5 feet, canned is $10 with a volume of 2 feet.
a)How much of each kind of beer should you buy if you want to spend your whole budget and use all remaining space?
b)Graph equations for capacity and cost and show intersection point on the graph. Be sure to label your graph and clearly show your scale.


I have created the formulas 540=12x +10y and 110=2.5x +2y

Using the first formula and trial and error, i find values for x and y, and by entering them into the second formula, I can see if they work. By doing so I have found that 20 Bottled and 30 Canned cases meets the space and cost requirements. I just totally forget how to proceed from here to part B. Its been about 11 years since I took math 11 and I am a little rusty, could it be that the method |I used is not the preferred method and there is an easier or more correct formula I could then graph? Taking a business assessment test tomorrow and this is the only question I had issue with, please help as I'm not sure how many of these graphing questions are going to be on said test. Thanks.

The equations are correct but for the graph, you can turn your equations around and write
y_c = 54 - 1.2x
for the cost graph and
y_s = 55 - 1.25x
for the space graph.

Where the two graphs intersect, both conditions are satisfied. The point where they intersect is y_c = y_s, so if you solve that equation for x, you can compute where both conditions are satisfied.

 

[stapel]

The equations are correct but for the graph, you can turn your equations around and write
y_c = 54 - 1.2x
for the cost graph and
y_s = 55 - 1.25x
for the space graph.

Where the two graphs intersect, both conditions are satisfied. The point where they intersect is y_c = y_s, so if you solve that equation for x, you can compute where both conditions are satisfied.

FYI to original poster:

Where the post (quoted above) refers to "turning your equations around", the poster is talking about solving literal equations (in the second link provided earlier).

Where the post refers to "where the two [lines] intersect, both conditions are satisfied", the poster is talking about solving the system of linear equations by graphing (in the first link provided earlier).

You should expect to need to solve systems with more than just two equations with more than just two variables, so you'll want to learn to algebraic (as opposed to graphing) methods, too.