Question

Every sack of sugar has the same weight. Every sack of flour has the same weight, but not necessarily the same as the weight of the sacks of sugar. Suppose that three sacks of sugar together with four sacks of flour weighs no more than 50 pounds, and that the weight of two sacks of flour is no more than 13 pounds more than the weight of three sacks of sugar. What is the largest possible weight (in pounds) of a sack of flour?

Answer 1

3s+4f <= 50
2f <= 13+3s

so,

4f <= 6s+26

3s+4f <= 3s+6s+26 <= 50
9s <= 24
s <= 8/3

So, since the smallest s gives the largest f in

3s+4f <= 50
8 + 4f <= 50
4f <= 42
f <= 21/2

Max f is 21/2