1 cat 1 eat 35/7/4= 1.25 yuan cat food every day;

1 dog 1 eat 5 yuan dog food 27/6/3 =1.

The daily food expenditure of three cats and seven dogs is1.25 * 3+1.5 * 7 =14.25 yuan;

250/ 14.25= 17.54 days;

Suppose 250 yuan can feed them for 17 days at most.

What is the board fee for three cats 17 days?

1.25*3* 17=63.75 yuan.

A bag of cat food, 35 yuan. Buy the whole bag.

63.75/35= 1.82

Need to buy 2 bags of cat food, the actual cost is 35*2=70 yuan.

The food cost for 7 dogs 17 days is

1.5 * 7 *17 =178.5 yuan.

A bag of dog food, 27 yuan. Buy the whole bag.

178.5/27=6.6

I need to buy 7 bags of dog food, and the actual cost is 27*7= 189 yuan.

Then the total cost of 17 days is 70+ 189=259 yuan, which exceeds the budget and needs to buy a bag of cat food or dog food less.

Buy one less bag of cat food, and the cat food you buy can feed three cats at most for 35/3/ 1.25=9.33 days.

Buy one less bag of dog food, and the dog food you buy is enough for 7 dogs to eat for 27*6/7/ 1.5= 15.43 days at most.

Therefore, it is enough to buy a bag of dog food for a few days at most, and 250 yuan is enough for them to eat at most 15 days.