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?

ghistory Aug 3, 2024

#1**0 **

Let S represent the weight of one sack of sugar.

Let F represent the weight of one sack of flour.

Two sacks of suagr together with three sacks of lour weight no more than 40 pounds:

2S + 5F <= 60

The weight of a sack of flour is no more than 5 poiunds more than the weight of two sacks of sugar:

F <= 2S + 8

Since both of the inequalities have the same sense (point in the same direction), we can substitute:

Substituting: 2S + 3(2S + 5) <= 40

2S + 6S + 15 <= 40

8S + 15 <= 40

8S <= 25

S <= 3.125

Since F <= 2S + 5 ---> F <= 2(3.125) + 5 ---> F <= 11.25

So, each sack of flour cannot weigh more than 11.25 pounds.

Rangcr897 Aug 4, 2024