Answer:
a) see below for a graph
b) refer to the definition of the variables for the interpretation of the intercepts
Explanation:
a) The equation can be rewritten to intercept form by dividing by 192.
x/(192/8) + y/(192/12) = 1
x/24 + y/16 = 1
This equation tells you the x-intercept is 24, and the y-intercept is 16. Plot those points and draw a straight line between them. (x- and y-values that are negative have no meaning in this problem.)
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b) What? There are no variable definitions? So, we have to figure out the meaning of the variables based on the context.
If buns are sold in packages of 8, the term 8x might stand for the number of buns in x packages of 8. Likewise, for buns sold in packages of 12, the number 12y might stand for the number of buns in y packages of 12. Then the sum of these two terms being 192 might model the tradeoff between packages of 8 and packages of 12 when we want a total of 192 buns.
So, the x-intercept is the point where y=0. It would be the number of packages of 8 buns required if only that kind of package were purchased. It is 24, so 24 packages of 8 buns would satisfy the requirement for 192 buns.
Likewise, the y-intercept is the point where x=0. It would be the number of packages of 12 buns required if only that kind of package were purchased. It is 16, so 16 packages of 12 buns would satisfy the requirement for 192 buns.
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Comment on this question
Increasingly, we see questions like this where the variables of the problem are not defined as they should be. One should always begin the solution of a problem such as this with ...
- a definition of the variables being used
- a definition of the units associated with any numerical values (or variables)