In part a, you determined that you can make 40 servings from five packages of buns and four packages of hot dogs without anything left over. this means that you can also make 80, 120, 160, and so forth, servings without anything left over. these numbers are called multiples of 40.you need to find the smallest integer multiple of 40 that is greater than or equal to 700. then, use this to determine the number of packages of buns and hot dogs.

ceiling(700/40) = ceiling(17.5) = 18 . . . . ceiling(x) is the smallest integer ≥ x.

The smallest integer multiple of 40 that is larger than 700 is 18.

The number of packages of buns will be 18*5 = 90.

The number of packages of hotdogs will be 18*4 = 72.

These numbers will ensure that you have 20 bun/hotdog combinations left over. If you want to minimize leftovers, you would use 88 packages of buns and 70 packages of hotdogs. That would give you 4 buns and no hotdogs left over.

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