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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
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
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