Let

'x' = the number of oranges to purchase by $0.69 cost

'y' = the number of grapefruits to purchase by $0.96 cost

x*0.69 + y*0.96 = 15.76 multiply both sides by 100

x*69 + y*96 = 1576

y = (1576 - 69*x)/96

also x and y need to be non-negative numbers that is

1576 - 69x >=0

1576 / 69 >= x

22 + 58/69 > =x

1576 - 96*y >=0

1576 / 96 >= y

16 + 5/12 >= y

This means i have to order not more then (22 + 58/69) oranges and not more then (16 + 5/12) grapefruits and if the order has x oranges then it must have (1576 - 69*x)/96 grapefruits.

One solution would be

For x =10 that is if I order 10 oranges then I need to purchase y = (1576 - 69*x)/96 = (1576 - 690) / 96 = 886/96 = 443/48 grapefruits.