Let a be the number of 25-CD spindles and b be the number of 60-CD spindles, then 25a+60b=230.
Divide through by 5:
5a+12b=46, so a=(46-12b)/5.
From this we can see that 46-12b must be positive, otherwise a would be negative. Therefore, 46-12b>0, 46>12b, 46/12>b, 23/6>b, or b<23/6, that is, b<3⅚, so b must be less than or equal to 3.
If b=3, a=(46-36)/5=10/5=2. So we have a solution: a=2, b=3.
25×2+60×3=50+180=230.
So she needs 2 25-CD and 3 60-CD spindles.