Experts Please Help

Question

Problem: You own an orchard of apple trees. From experience, you know that when 100 trees are planted, each tree yields approximately 240 apples. Furthermore, you’ve also noticed that when an additional tree is planted, the yield per tree decreases by about 20 apples for each additional tree.

1. If x is the number of additional trees planted, write a formula for the number of trees
2. If x is the number of additional trees planted, write a formula for the number of apples produced by each tree.
3. If x is the number of additional trees planted, write a formula for the number of apples produced by all the trees. 

Be sure to clearly show all your work, formulas used, and justify each step. 

Answer 1

The purpose of this question is to practice writing expressions, and then putting those expressions to use. Notice that each bullet describes a step toward answering the most important question the farmer would ask, "How many apples can I expect?" Let's address each bullet in turn.

1. If we start with 100 trees and add x trees the number of trees becomes (100 + x). That was easy.
2. Before overcrowding each tree can produce 240 apples, but for EACH tree added the number of apples per tree is reduced by 20. Therefore, if x trees are added, the number of apples per tree can be expressed as (240 - 20x).
3. Now that we have expressions for the number of trees and the number of apples per tree, we can multiply these to determine the total number of apples. The total number of apples can be found as (100 + x)(240 - 20x)

Since the problem wasn't specific about what form the answer should take, we're done.