Let x represent the number of apples and y the number of oranges.
Starting with the first scenario, since each apple is priced at $0.24 and each orange at $0.80, we have:
total spent on apples = 0.24x and total spent on oranges = 0.8y
Given that the total expenditure is $12, the first equation is:
0.24x + 0.8y = 12
For the second scenario, the total number of pieces of fruit purchased is 20, thus the second equation is:
x + y = 20
By graphing these equations, one can identify a potential combination at the intersection of the two lines.