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 $5$ pounds more than the weight of two sacks of sugar. What is the largest possible weight (in pounds) of a sack of flour?

The LARGEST POSSIBLE SACK of flour  is 11.24  pounds.

Step-by-step explanation:

Let us assume the weight of 1 sack of sugar  = m pounds

And the weight of 1 sack of flour = n pounds

Now, weight of 2 sacks of sugar  = 2 x ( Weight of 1 sack of sugar)

                                                       = 2 x (m)    = 2 m

Also, weight of 3 sacks of flour  = 3 x ( Weight of 1 sack of flour)

                                                       = 3 x (n)    = 3 n

Given : Weight of (2 sacks of sugar  +  3 sacks of flour) ≤ 40 pounds

⇒ 2  m +  3 n  ≤ 40 (1)

Similarly, Weight of (1 sack of flour) ≤  2 sacks of sugar  +  5 pounds

⇒ n   ≤  2 m  + 5   (2)

Now, solving (1) and (2) for the values of m and n, we get:

2  m +  3 n  ≤ 40

n   ≤  2 m  + 5

Put  n  = 2 m  + 5 in (1)

We get: 2  m +  3 n  = 40  ⇒ 2  m +  3 (2 m  + 5)   = 40

or, 2 m + 6 m + 15 = 40

or, 8 m = 25

or, m = 25/8   =   3.12

So,  m  CAN NOT BE MORE THAN 3.12 pounds

Solving for n = 2 m + 5 = 2(3.12) + 5  = 11.24 pounds

So,  n  CAN NOT BE MORE THAN  11.24  pounds

Hence, the LARGEST POSSIBLE SACK of flour  is 11.24  pounds.