Question

There are two formulae you can use to calculate the number of apple trees and the number of conifer

trees for the pattern described on the previous page:
Number of apple trees = n2
Number of conifer trees = 8n
where n is the number of rows of apple trees
There is a value of n for which the number of apple trees equals the number of conifer trees.
Find the value of n and show your method of calculating this.​

Answer 1

9514 1404 393

Answer:

n = 8

Explanation:

"By inspection" is an appropriate method.

We are asked to compare the expressions

n·n

8·n

and find the value(s) of n that makes them equal. By inspection, we see that n=8 will make these expressions equal. We also know that both expressions will be zero when n=0.

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More formally, we could write ...

n^2 = 8n . . . . the two formulas give the same value

n^2 -8n = 0 . . . . rearrange to standard form

n(n -8) = 0 . . . . . factor

Using the zero product rule, we know the solutions will be the values of n that make the factors zero. Those values are ...

n = 0 . . . . . makes the factor n = 0

n = 8 . . . . . makes the factor (n-8) = 0

Generally, we're not interested in "trivial" solutions (n=0), so the only value of n that is of interest is n = 8.

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A lot of times, I find a graphing calculator to be a quick and easy way to find function argument values that make expressions equal.