SOLUTION: PLEASE HELP ME WITH THIS PROBLEM< ITS MY LAST ONE AND I'M STUCK!!!! ***I NEED THE STEPS TO SOLVE THIS PROBLEM SO THAT I CAN BETTER UNDERSTAND IT...PLEASE HELP*** ANSWER: 36

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Question 385120: PLEASE HELP ME WITH THIS PROBLEM< ITS MY LAST ONE AND I'M STUCK!!!!
***I NEED THE STEPS TO SOLVE THIS PROBLEM SO THAT I CAN BETTER UNDERSTAND IT...PLEASE HELP***
ANSWER: 36 to 38trees/acre
PROBLEM: PLANTING AN APPLE ORCHARD
The owner of an apple orchard estimates that if 24trees are planted per acre, then each mature tree will yield 600 apples per year. For each additional tree planted per acre, the number of apples produced by each tree decreases by 12 per year. How many trees should be planted per acre to obtain at least 16,417 apples per year?
THANK YOU!!!!!!!!
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The owner of an apple orchard estimates that if 24trees are planted per acre,
then each mature tree will yield 600 apples per year.
For each additional tree planted per acre, the number of apples produced by
each tree decreases by 12 per year.
How many trees should be planted per acre to obtain at least 16,417 apples per year?
:
Let x = no. of trees added the 24 existing trees
and
x = no. of 12 apple decreases from original 600 per tree
:
Write an equation representing the total number of apples obtained
(24+x)*(600-12x) = 16417
FOIL
14400 - 288x + 600x - 12x^2 = 16417
Combine like terms to form a quadratic equation
-12x^2 + 312x + 14400 - 16417 = 0
-12x^2 + 312x - 2017 = 0
Use the quadratic formula to find x: a=-12; b=312; c=-2017

Do the math; you should get two solutions; (Round to an integer value)
x ~ 14, x ~ 12 trees, which when added to 24 will give you the 36 - 38 trees