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 three sacks of flour weigh no more than 40 pounds, and that the weight of a sack of flour is no more than 6 pounds more than the weight of two sacks of sugar. What is the largest possible weight (in pounds) of a sack of flour?
Let x be the weight of a sack of sugar
Let y be the weight of a sack of flour
We have these inequalities
2x + 3y ≤ 40
y - 2x ≤ 6
See the graph here : https://www.desmos.com/calculator/rlbzlpxzgz
The max weight of a sack of flour occurs at the "corner point" of the feasible region = 11.25 lbs