Question

Juan has 7 1/2 cups of chopped almonds. He wants to make banana muffins and apple cinnamon muffins. He needs a 1/2 cup of almonds and 5/8 cups of almonds for each batch of apple cinnamon muffins. How many total batches of muffins can he make?​

Answer 1

if he makes b batches of banana and a batches of apple, then
1/2 b + 5/8 a <= 7 1/2
or, to avoid the fractions,
4b + 5a <= 60
There are several combinations which can be made (assuming an even number of batches for each kind):
b a
0 12
5 8
10 4
15 0