Let's solve this problem step by step.
1. Understanding the relationships:
- 1 drachm is equivalent to 15 denarii.
- 1 drachm is equivalent to approximately 12.27 grams.
- 10 grams are equivalent to 1 decagram.
2. Convert denarii to drachms:
- We are given 49 denarii.
- To find out how many drachms this is equivalent to, we divide the number of denarii by the number of denarii per drachm.
[tex]\[
\text{Drachms} = \frac{\text{Denarii}}{\text{Denarii per Drachm}} = \frac{49}{15} \approx 3.2667 \ \text{(rounded to 4 decimal places for intermediate values)}
\][/tex]
3. Convert drachms to grams:
- We have approximately 3.2667 drachms.
- To find out how many grams this equates to, we multiply the number of drachms by the number of grams per drachm.
[tex]\[
\text{Grams} = \text{Drachms} \times \text{Grams per Drachm} = 3.2667 \times 12.27 \approx 40.082 \ \text{grams}
\][/tex]
4. Convert grams to decagrams:
- We have approximately 40.082 grams.
- To find out how many decagrams this equates to, we divide the number of grams by the number of grams per decagram.
[tex]\[
\text{Decagrams} = \frac{\text{Grams}}{\text{Grams per Decagram}} = \frac{40.082}{10} \approx 4.0082
\][/tex]
5. Round to the nearest hundredth:
- We need to round the number of decagrams to the nearest hundredth.
[tex]\[
\text{Decagrams (rounded)} = 4.01
\][/tex]
Therefore, 49 denarii are approximately equivalent to 4.01 decagrams when rounded to the nearest hundredth.
