Let's solve the problem step-by-step to understand how many pounds of tomatoes can fit into one crate.
1. Understand the given problem:
- A vegetable farmer fills [tex]\(\frac{2}{3}\)[/tex] of a wooden crate with [tex]\(\frac{5}{7}\)[/tex] of a pound of tomatoes.
- We need to find the total weight of tomatoes that can fill a complete crate.
2. Calculate the weight of tomatoes in one full crate:
- If [tex]\(\frac{2}{3}\)[/tex] of a crate is filled with [tex]\(\frac{5}{7}\)[/tex] of a pound of tomatoes, we need to find how many pounds would fill the entire crate.
- To find this, we divide the weight of the tomatoes by the fraction of the crate they fill.
3. Perform the division:
[tex]\[
\text{Weight per full crate} = \frac{\frac{5}{7}}{\frac{2}{3}} = \frac{5}{7} \times \frac{3}{2} = \frac{5 \cdot 3}{7 \cdot 2} = \frac{15}{14}
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{15}{14} = 1 \frac{1}{14}
\][/tex]
5. Compare the simplified result with the given choices:
The simplified result is [tex]\(1 \frac{1}{14}\)[/tex] pounds, which matches choice B.
So, the correct answer is:
[tex]\[ B. 1 \frac{1}{14} \text{ pounds} \][/tex]
