Certainly! Let's solve this step-by-step:
1. Define Variables:
- Let [tex]\( x \)[/tex] be the number of fruit-bearing trees.
- Let [tex]\( y \)[/tex] be the number of non-fruit-bearing trees.
2. Form the Equations:
- According to the problem, the total number of trees is 102. Thus,
[tex]\[ x + y = 102 \][/tex]
- The number of non-fruit-bearing trees is described as two more than thrice the number of fruit-bearing trees. In other words:
[tex]\[ y = 3x + 2 \][/tex]
3. Substitute the Second Equation into the First:
- Replace [tex]\( y \)[/tex] in the first equation with [tex]\( 3x + 2 \)[/tex]:
[tex]\[ x + (3x + 2) = 102 \][/tex]
4. Simplify and Solve for [tex]\( x \)[/tex]:
- Combine like terms:
[tex]\[ 4x + 2 = 102 \][/tex]
- Subtract 2 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 4x = 100 \][/tex]
- Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 25 \][/tex]
So, the number of fruit-bearing trees that were planted is 25.
5. Calculate the Number of Non-Fruit-Bearing Trees:
- Using the equation [tex]\( y = 3x + 2 \)[/tex]:
[tex]\[ y = 3(25) + 2 \][/tex]
[tex]\[ y = 75 + 2 \][/tex]
[tex]\[ y = 77 \][/tex]
Therefore, the number of non-fruit-bearing trees is 77.
To summarize:
- Number of fruit-bearing trees = [tex]\( 25 \)[/tex]
- Number of non-fruit-bearing trees = [tex]\( 77 \)[/tex]
This aligns with the total number of trees being 102:
[tex]\[ 25 + 77 = 102 \][/tex]
Thus, the solution is correct.
