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?
For this, we can make an inequality. So, here is what we have, according to the question:
2 sacks of sugar + 3 sacks of flour \(\leq\) 40 lbs
flour \(\leq\) 2 sacks of sugar + 6lbs
Using variable form, this is:
2s + 3f \leq 40
f \leq 2s+6
Since the question is asking for the largest possible weight, we can change the /leq to equal signs
2s + 3f = 40
f = 2s+6
Now, we can isolate the two stacks of sugar. So:
f-6 = 2s
40-3f = 2s
Now, our equation is:
f = 11.5 lbs
Therefore, the flour weighs 11.5 lbs.