It appears you have multiple questions here. Let's focus on the grain packets question.
Given two packets of grain with weights [tex]\(3 \frac{4}{7} \, \text{kg}\)[/tex] and [tex]\(5 \frac{2}{5} \, \text{kg}\)[/tex], and knowing that [tex]\(2 \frac{1}{7} \, \text{kg}\)[/tex] was removed after mixing the grains together, we need to determine how much grain is left.
Let's proceed step by step:
1. Convert the weights of the grain packets to improper fractions:
- For the first packet: [tex]\(3 \frac{4}{7}\)[/tex]
[tex]\[
3 \frac{4}{7} = 3 + \frac{4}{7} = \frac{21}{7} + \frac{4}{7} = \frac{25}{7}
\][/tex]
- For the second packet: [tex]\(5 \frac{2}{5}\)[/tex]
[tex]\[
5 \frac{2}{5} = 5 + \frac{2}{5} = \frac{25}{5} + \frac{2}{5} = \frac{27}{5}
\][/tex]
2. Convert the amount of grain removed to an improper fraction:
- For the removed grain: [tex]\(2 \frac{1}{7}\)[/tex]
[tex]\[
2 \frac{1}{7} = 2 + \frac{1}{7} = \frac{14}{7} + \frac{1}{7} = \frac{15}{7}
\][/tex]
3. Calculate the total weight of the grain by adding the initial weights:
- Combine the fractions:
[tex]\[
\frac{25}{7} + \frac{27}{5}
\][/tex]
To do this, we find a common denominator, which is [tex]\(35\)[/tex]:
[tex]\[
\frac{25}{7} = \frac{25 \times 5}{7 \times 5} = \frac{125}{35}
\][/tex]
[tex]\[
\frac{27}{5} = \frac{27 \times 7}{5 \times 7} = \frac{189}{35}
\][/tex]
Now add them together:
[tex]\[
\frac{125}{35} + \frac{189}{35} = \frac{314}{35}
\][/tex]
4. Subtract the weight of the grain removed:
- Convert the removed fraction to the common denominator:
[tex]\[
\frac{15}{7} = \frac{15 \times 5}{7 \times 5} = \frac{75}{35}
\][/tex]
- Subtract this from the total:
[tex]\[
\frac{314}{35} - \frac{75}{35} = \frac{314 - 75}{35} = \frac{239}{35}
\][/tex]
5. Convert the result back to a mixed number:
- Divide [tex]\(239\)[/tex] by [tex]\(35\)[/tex]:
[tex]\[
239 \div 35 = 6 \text{ remainder } 29
\][/tex]
So,
[tex]\[
\frac{239}{35} = 6 \frac{29}{35}
\][/tex]
Therefore, the total amount of grain left after removing [tex]\(2 \frac{1}{7} \, \text{kg}\)[/tex] from the mixed packets is:
[tex]\(
6 \frac{29}{35} \, \text{kg}
\)[/tex].
The numerical result from the calculations shows that the total grain initially mixed together was approximately [tex]\(8.971 \, \text{kg}\)[/tex], and the grain left after removal is around [tex]\(6.829 \, \text{kg}\)[/tex].
