Answer:
Explanation:
Let's assume that the original arrangement had x rows and y columns, so the total number of trees would be x*y.
According to the problem, if there were 5 more rows and 3 fewer columns, the new arrangement would have x+5 rows and y-3 columns, and the total number of trees would be (x+5)*(y-3).
We also know that the difference in the number of trees between the two arrangements is 25. Therefore, we can write:
(x+5)(y-3) - xy = 25
Expanding the terms, we get:
xy - 3x + 5y - 15 - xy = 25
Simplifying, we get:
2y - 3x = 40
We need to find the values of x and y that satisfy this equation and represent the number of rows and columns in the original arrangement.
One possible way to do this is to try different values of y and see if we can find an integer value of x that satisfies the equation. For example, if we set y=14, then:
2y - 3x = 40
2(14) - 3x = 40
28 - 3x = 40
-3x = 12
x = -4
This value of x is not valid because we cannot have a negative number of rows. Let's try another value of y, say y=15:
2y - 3x = 40
2(15) - 3x = 40
30 - 3x = 40
-3x = 10
x = -10/3
Again, this value of x is not valid because we cannot have a fraction of a row. Let's try another value of y, say y=16:
2y - 3x = 40
2(16) - 3x = 40
32 - 3x = 40
-3x = 8
x = -8/3
Once again, this value of x is not valid. We can continue trying different values of y, but we can also notice that the left-hand side of the equation, 2y - 3x, is always odd because 2y is even and 3x is odd. Therefore, the right-hand side, 40, must be odd as well, which is impossible.
Therefore, there is no solution to this problem, and we cannot determine how many apple trees the farmer has planted.