Question

All sacks of sugar have the same weight. All sacks of flour also have the same weight, but not necessarily the same as the weight of the sacks of sugar. Suppose that two sacks of sugar together with five sacks of flour weigh no more than $60$ pounds, and that the weight of a sack of flour is no more than $8$ pounds more than the weight of two sacks of sugar. What is the largest possible weight (in pounds) of a sack of flour?

Answer 1

Let s be the weight of a sack of sugar and f the weight of a sack of flour. The conditions give
2s + 5f ≤ 60 and f ≤ 2s + 8, so s ≥ (f − 8)/2. Thus
(f − 8)/2 ≤ 30 − 2.5f.
Multiply by 2: f − 8 ≤ 60 − 5f ⇒ 6f ≤ 68 ⇒ f ≤ 68/6 = 34/3.

This value is attainable when 2s + 5f = 60 and f = 2s + 8, which yields s = 5/3 and f = 34/3. Hence the largest possible weight of a sack of flour is 34/3 pounds.