+2669 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?
+399 weight of sugar = s
weight of flour = f
\(\begin{cases} 2s+3f \le 40 \\ f \le 6 + 2s \end{cases}\)
\(\begin{cases} (2s)+3f \le 40 \\ f - 6\le (2s) \end{cases}\)
\(f-6 + 3f \le 2s+3f\le40\)
\(4f-6\le 40\)
\(4f\le46\)
\(f\le\frac{23}{2}\)
23/2 pounds is greatest solution, this occurs when \(f-6=2s\), \(s=\frac{11}{4}\). (always make sure to check the solution works with inequalities).
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+399 weight of sugar = s
weight of flour = f
\(\begin{cases} 2s+3f \le 40 \\ f \le 6 + 2s \end{cases}\)
\(\begin{cases} (2s)+3f \le 40 \\ f - 6\le (2s) \end{cases}\)
\(f-6 + 3f \le 2s+3f\le40\)
\(4f-6\le 40\)
\(4f\le46\)
\(f\le\frac{23}{2}\)
23/2 pounds is greatest solution, this occurs when \(f-6=2s\), \(s=\frac{11}{4}\). (always make sure to check the solution works with inequalities).
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