To determine the number of rows of trees in the parcel, we need to use the given information and set up an equation. Let's break it down step by step:
1. Number of Trees per Row:
Each row has [tex]\( 3x - 2 \)[/tex] trees. This expression represents the number of trees in one row.
2. Total Number of Trees:
There are [tex]\( 24x - 16 \)[/tex] trees planted in the entire parcel. This expression represents the total number of trees in all rows combined.
3. Number of Rows:
Let [tex]\( r \)[/tex] represent the number of rows of trees in the parcel. We can set up the equation:
[tex]\[
r \times (3x - 2) = 24x - 16
\][/tex]
Here, [tex]\( r \)[/tex] times the number of trees per row should equal the total number of trees.
4. Solving for [tex]\( r \)[/tex]:
We can solve for [tex]\( r \)[/tex] by dividing both sides of the equation by [tex]\( 3x - 2 \)[/tex]:
[tex]\[
r = \frac{24x - 16}{3x - 2}
\][/tex]
5. Simplifying the Expression:
The simplified form of the expression is the number of rows:
[tex]\[
r = \frac{24x - 16}{3x - 2}
\][/tex]
Thus, the number of rows of trees in the parcel is given by:
[tex]\[
\frac{24x - 16}{3x - 2}
\][/tex]
Now, let's match this result to the given answer choices:
a. [tex]\( 21x - 18 \)[/tex]
b. [tex]\( 21x - 14 \)[/tex]
c. [tex]\( 8x \)[/tex]
d. [tex]\( 8 \)[/tex]
The correct answer is:
[tex]\[
\frac{24x - 16}{3x - 2}
\][/tex]
When comparing this result to the answer choices, we can see that none of them match the given expression exactly. Therefore, the correct option is not listed among the provided choices.
