When there are 22 apple trees per acre, the average yield has been found to be 700 apples per tree. For each additional tree planted per acre, the yield per tree decreases by 12 apples per tree. How many additional trees per acre should be planted to maximize the yield? (Round your answer to the nearest whole number.)

Question

anonymous · Answer

This looks like a prob I posted on here last time, but when I tried solving the same way, I didn't get the right answer.

anonymous · Answer

TuringTest, I solved it the way you showed me how to solve this other prob last time...

turingtest · Answer

Yes I figured you were referring to that problem. I agree that it should be the same, so let's just see what we get.

turingtest · Answer

A=total number of apples
r=original average yield per tree=700
t=number of trees per acre
n=number of additional trees per acre

$$r={A \over t}={A \over 22}=700\to A=15400$$our statement can be interpreted as$$r-12n={A \over t+n}$$plugging in the numbers gives$$700-12n={15400 \over 22+n}$$is this how yours was set up?

turingtest · Answer

*above should be:
t=original number of trees per acre=22

anonymous · Answer

I have it just like that except I have 700-n not 700-12n

turingtest · Answer

Well there's your problem.

Our last problem had the average sales decreasing by 1 for each additional store, I remember. This has a decrease of 12 apples per each additional tree, so it needs to be 12n, not n. 

You should get the right answer now.

anonymous · Answer

Ok, I see what I did wrong.

anonymous · Answer

I got 240 but its wrong

turingtest · Answer

let me see what I get...

anonymous · Answer

i get 22+218=240 in the end

turingtest · Answer

well this time it only wants the number of additional trees, so you would just use the number you get for n=218
did you try that?

anonymous · Answer

thats wrong too :(

turingtest · Answer

that's not the answer I'm getting anyway, I got $$n \approx18$$so try that, if it's right we'll see where you went wrong.

anonymous · Answer

yeah, its 18

anonymous · Answer

show me what u did so i can compare

anonymous · Answer

i think i did the last part wrong

anonymous · Answer

the part after -n^2+436n=0

turingtest · Answer

huzzah! ok lets see where you went wrong.
we had$$700-12n={15400\over 22+n}$$multiply both sides by 22+n:$$(700-12n)(22+n)=15400$$simplify$$15400+700n-264n-12n^2=15400$$$$436n-12n^2=0$$using the formula you used last time with a=-12 and b=436 $${-b \over2a}={-436\over-24}\approx18$$and there we have it :) 
questions, comments, outbursts?

turingtest · Answer

yes it seems you lost the twelve...

anonymous · Answer

hold on lol

anonymous · Answer

Ok... yeah it was the 12 again...

anonymous · Answer

didnt plug it in everywhere and it messed up my answer

turingtest · Answer

Just read problems carefully, don't just recognize it's of the same form as one you have done before, notice details. 

Think about what it means to lose twelve apples on average per tree planted.

Those details can make or break you, but congrads for recognizing the problem was very similar. Good job, I'm sure you'll do fine in your class :)

anonymous · Answer

Thanks. I appreciate your assistance.

turingtest · Answer

Gladly!