SOLUTION: An orchard has 728 pear trees. The number of rows exceeds the number of trees per row by 2. How many trees are there in each row?

Question 1179483: An orchard has 728 pear trees. The number of rows exceeds the number of trees per row by 2. How many trees are there in each row?

Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

An orchard has pear trees.
The number of rows exceeds the number of trees per row by .

...........substitute

...take only positive solution

there are rows, and trees per row

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Note in the solution from the other tutor how the standard algebraic solution involves factoring the quadratic equation

Few people are going to look at that and see that the factorization is

In their solution, they solved the equation using the quadratic formula. That always works; but in this case it still involved working with large numbers.

This is an example of a problem where a bit of insight (or perhaps a lot of experience) can make solving the problem much easier.

Here is what I saw almost immediately on reading the problem: we have two numbers that differ by 2 whose product is 728. That is two numbers that are very close together, so the 728 is very close to a perfect square. So instead of calling the numbers x and x+2....

let x-1 be the smaller number (number of trees per row)
let x+1 be the larger number (number of rows of trees)

Then the given information yields an equation that is solved relatively easily:

ANSWER: The number of trees in each row is x-1=26

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