Darcy is buying apples and oranges for a large fruit basket to give away as a door prize at a charity event. apples cost $.24 each and oranges cost $.80 each. she has $12 to spend and would like to purchase at least 20 pieces of fruit total

Let x be the number of apples 
Let y be the number of oranges 

x+y≤20 
0.24x+0.8y≤12

x≤20-y 

0.24(20-y)+0.8y≤12
4.8-0.24y+0.8y≤12
0.56y≤7.2
y=12.9 (you can choose 12 here, since you can't have a fraction of an orange sold) 

x= 7.14 (again, rounding this off to 7) 

Therefore, Darcy got 12 oranges and 7 apples. 

Hope I helped :)