To determine how many pounds of tomatoes can fit into a fully filled wooden crate, we start with the information given:
- The farmer fills [tex]\(\frac{2}{3}\)[/tex] of a wooden crate with [tex]\(\frac{5}{7}\)[/tex] of a pound of tomatoes.
We are asked to find out the total pounds of tomatoes that a fully filled crate can hold. Let's denote the full capacity of the crate in pounds with [tex]\( x \)[/tex].
Given that [tex]\(\frac{2}{3}\)[/tex] of the crate holds [tex]\(\frac{5}{7}\)[/tex] pounds of tomatoes, we set up the equation:
[tex]\[
\frac{2}{3} \times x = \frac{5}{7}
\][/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]. We do this by dividing both sides of the equation by [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
x = \frac{\frac{5}{7}}{\frac{2}{3}}
\][/tex]
Dividing by a fraction is equivalent to multiplying by its reciprocal, so:
[tex]\[
x = \frac{5}{7} \times \frac{3}{2}
\][/tex]
Next, we multiply the fractions:
[tex]\[
x = \frac{5 \times 3}{7 \times 2} = \frac{15}{14}
\][/tex]
To convert [tex]\(\frac{15}{14}\)[/tex] into a mixed number, we perform the division [tex]\( 15 \div 14 \)[/tex]:
- 15 divided by 14 equals 1 with a remainder of 1.
Thus, we can express [tex]\(\frac{15}{14}\)[/tex] as a mixed number:
[tex]\[
1 \frac{1}{14}
\][/tex]
So, the total pounds of tomatoes that can fit into one fully filled crate is [tex]\( 1 \frac{1}{14} \)[/tex] pounds.
The correct answer is:
A. [tex]\( 1 \frac{1}{14} \)[/tex] pounds
