To solve the problem, we need to determine the number of rows of trees in the parcel. Let's denote the number of rows by [tex]\( r \)[/tex].
Given:
- Number of trees in each row = [tex]\( 3x - 2 \)[/tex]
- Total number of trees = [tex]\( 24x - 16 \)[/tex]
To find the number of rows, we can set up the following equation since the total number of trees is equal to the number of rows multiplied by the number of trees per row:
[tex]\[
r \times (3x - 2) = 24x - 16
\][/tex]
Now, solve for [tex]\( r \)[/tex]:
1. Distribute [tex]\( r \)[/tex] on the left side:
[tex]\[
r(3x - 2) = 24x - 16
\][/tex]
2. To isolate [tex]\( r \)[/tex], divide both sides of the equation by [tex]\( 3x - 2 \)[/tex]:
[tex]\[
r = \frac{24x - 16}{3x - 2}
\][/tex]
From here, we need to simplify the fraction on the right-hand side. We can attempt to simplify by factoring or recognizing any patterns that may emerge:
3. Let's simplify the numerator [tex]\( 24x - 16 \)[/tex]. Notice that both terms in the numerator share a common factor of 8:
[tex]\[
24x - 16 = 8(3x - 2)
\][/tex]
4. Substitute [tex]\( 8(3x - 2) \)[/tex] back into our equation:
[tex]\[
r = \frac{8(3x - 2)}{3x - 2}
\][/tex]
5. Notice that the [tex]\( 3x - 2 \)[/tex] terms in the numerator and denominator cancel out:
[tex]\[
r = 8
\][/tex]
Thus, the number of rows of trees in the parcel is [tex]\( 8 \)[/tex].
So, the correct answer is:
d. 8
