Subjects algebra

Postal Rate

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1. **Stating the problem:** A letter costs Le 300 for the first gram and Le 50 for each additional half gram or part thereof. We need to find the total cost to post a letter weighing $w$ grams. 2. **Understanding the pricing rule:** - The first gram costs Le 300. - Every additional half gram or part of it costs Le 50. 3. **Formula and explanation:** Let $w$ be the weight of the letter in grams. - If $w \leq 1$, cost = Le 300. - If $w > 1$, the additional weight beyond the first gram is $w - 1$ grams. - Each additional half gram or part thereof costs Le 50. We calculate the number of half grams beyond the first gram as: $$n = \left\lceil \frac{w - 1}{0.5} \right\rceil$$ where $\lceil x \rceil$ is the ceiling function (rounding up). 4. **Total cost formula:** $$\text{Cost} = 300 + 50 \times n$$ 5. **Example:** If the letter weighs $w = 2.3$ grams: - Additional weight = $2.3 - 1 = 1.3$ grams - Number of half grams = $\left\lceil \frac{1.3}{0.5} \right\rceil = \left\lceil 2.6 \right\rceil = 3$ - Additional cost = $50 \times 3 = 150$ - Total cost = $300 + 150 = 450$ 6. **Conclusion:** To find the cost, plug in the weight $w$ into the formula above and calculate accordingly.