Brain Teasers
Orchard
Last year, the average number of apples on each tree equalled the number of trees in the orchard. However this year there were 640 less apples than last year's harvest. If the average number of apples per tree this year was 72, how many trees are there in my orchard?
Please Note: No extra trees have been planted or any removed! There are no tricks to this question.
Please Note: No extra trees have been planted or any removed! There are no tricks to this question.
Answer
There are 80 trees in my lovely little orchard.Let T = the number of trees and N = the total number of apples. Set up two equations, one for each year:
Last year: N/T = T or N = T^2
This year: (N-640)/T = 72
Substitute N = T^2 into the second equation to get: (T^2 - 640)/T = 72.
Multiplying both sides by T and rearranging gives you the polynomial: T^2 - 72*T - 640 = 0. Solving this gives roots of -8 and 80. Obviously, there can't be -8 trees in the orchard, so there must be 80.
Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments
bluedreama, that was was a silly comment. if you didn't like it, at least explain why. for me, it brought back memories of high school algebra, oh so many years ago...
i think the comment was deleted...
Cool, and didn't need the quadratic formula to solve either! Nice Job!
Interesting. easy if you know about quadratics.
To post a comment, please create an account and sign in.
Follow Braingle!