Find the formula of the fruits a garden gives when there are 20+x trees.

[zade]

There are 20 trees in a garden and each of them gives 60 kg fruits a year. With the rise of the number of trees the production decreases. This decrease is 2 kg in year for each tree(over the number 20). When there are 20+x trees how much fruits gives the garden?
I think the formula is (20+x)*60-2x, but I'm not sure at all.

 

[Ishuda]

There are 20 trees in a garden and each of them gives 60 kg fruits a year. With the rise of the number of trees the production decreases. This decrease is 2 kg in year for each tree(over the number 20). When there are 20+x trees how much fruits gives the garden?
I think the formula is (20+x)*60-2x, but I'm not sure at all.

Let
n = the number of trees = 20 + x
f = kg of fruit per tree
Then total amount of fruit is then
T = n f = (20+x) f.
So f is a function of n so that
f = 20 - 2 * (n-20) = 20 - 2 * x
The total amount of fruit is then what?

 

[lookagain]

Let
n = the number of trees = 20 + x
f = kg of fruit per tree
Then total amount of fruit is then
T = n f = (20+x) f.
So f is a function of n so that
f = 20 - 2 * (n-20) = 20 - 2 * x
The total amount of fruit is then what?

T would be (20 + x)(20 - 2x), but when x = 0 as a check, you have the total amount

of fruit as 400 kg. At 20 trees and 60 kg per tree to start out with, the total amount

of fruit then is 1,200 kg. You never addressed the 60 kg. in your formula.

I think the formula is (20+x)*60-2x, but I'm not sure at all.

zade, if x is the number of additional trees beyond 20, then the formula could be

(20 + x)(60 - 2x).