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

To maximize the weight of a flour sack, minimize sugar weight. Let S be sugar weight, F be flour weight. We have two inequalities: 3S + 4F ≤ 50 and 2F ≤ 13 + 3S. Solving, we find the maximum F is 11.25 pounds.

We're given two inequalities that constrain the weights of sugar (S) and flour (F):

Three sacks of sugar and four sacks of flour weigh no more than 50 pounds: 3S + 4F ≤ 50.

Two sacks of flour weigh no more than 13 pounds more than three sacks of sugar: 2F ≤ 13 + 3S.

To maximize the weight of a flour sack (F), we want to minimize the weight of a sugar sack (S) while still satisfying the inequalities.

Here's how we can solve for the maximum F:

• Isolate F: 2F ≤ 13 + 3S --> F ≤ 6.5 + 1.5S.
• Replace F with the maximum allowed value: 3S + 4(6.5 + 1.5S) ≤ 50.
• Combine terms and solve for S: 3S + 26 + 6S ≤ 50 --> 9S ≤ 24 --> S ≤ 2.67 (rounded to two decimal places).
• Using the minimum S value: F ≤ 6.5 + 1.5S ≤ 6.5 + 1.5 * 2.67 ≈ 11.25 pounds.

Therefore, the largest possible weight of a sack of flour is 11.25 pounds.