Number - Trees

[Guest]

An apple farmer has an estimation that if 24 trees are planted per acre, each tree will yield 600 apples per year. The number of apples per tree is reduced by 12 per year for each additional tree planted per acre. Determine number of trees to be planted per acre for a yield of at least 16,416 apples per year.

Note: number of acres not given.

[Guest]

Let N = number of trees added
(24 + N)x(600 - 12N) = 16416

Solving gives N = 12 trees added

So plant 36 trees per acre

[Guest]

Error last post....corrected...

Let N = number of trees added
(24 + N)x(600 - 12N) = 16416

Solving gives N = 12 or 14 trees added

So plant 36 trees per acre or 38 trees per acre

[Guest]

Is there another method of solving besides FOIL and a quadratic equation ? Thanks.

[Guest]

I assume you mean is there another way of solving the problem or do you mean is there another way of solving the equation derived from the facts of the problem.

Solving the problem....we are using algebra and have ended up with a quadratic equation to solve.
Quadratic can be solved by factorising, formulae, completing the square etc etc

We could have used Iteration.....a process of trying a sequence of repeated steps hopefully focusing in on a solution.
That is try a range values for "apples per acre" and work out each time id it satisfies the result or is getting nearer it.