Sure, let's solve the problem step-by-step:
1. Convert Mixed Numbers to Improper Fractions:
- The amount of fertilizer is [tex]\(3 \frac{3}{4}\)[/tex] kg.
[tex]\[
3 \frac{3}{4} = 3 + \frac{3}{4} = \frac{3 \times 4}{4} + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4} \text{ kg}
\][/tex]
- The area of the field is [tex]\(3 \frac{1}{8}\)[/tex] square meters.
[tex]\[
3 \frac{1}{8} = 3 + \frac{1}{8} = \frac{3 \times 8}{8} + \frac{1}{8} = \frac{24}{8} + \frac{1}{8} = \frac{25}{8} \text{ m}^2
\][/tex]
2. Convert Improper Fractions to Decimal Form:
- For the amount of fertilizer:
[tex]\[
\frac{15}{4} = 3.75 \text{ kg}
\][/tex]
- For the field area:
[tex]\[
\frac{25}{8} = 3.125 \text{ m}^2
\][/tex]
3. Calculate the Number of Square Meters per Kilogram of Fertilizer:
- To find out how many square meters can be covered per 1 kg of fertilizer, we divide the total area by the total amount of fertilizer.
[tex]\[
\text{Area per kg} = \frac{\text{Total Field Area (m}^2\text{)}}{\text{Total Amount of Fertilizer (kg)}}
\][/tex]
- Plug in the values:
[tex]\[
\text{Area per kg} = \frac{3.125 \text{ m}^2}{3.75 \text{ kg}} \approx 0.8333333333333334 \text{ m}^2/\text{kg}
\][/tex]
Therefore, Anthony can spread fertilizer over approximately [tex]\(0.8333333333333334\)[/tex] square meters per 1 kg of fertilizer.
