Question

Tree enthusiasts use a point system to compare trees. They assign a number of points for each inch of circumference, foot of height, and foot of crown spread. The table shows the points in each category and the total points for three of South Carolina's trees. How many points are assigned to one unit of each measurement?

Answer 1

A)circumference: 1 point; height: 2 points; crown spread: 0.25 point
B)circumference: 1 point; height: 1 point; crown spread: 0.25 point
C)circumference: 1 point; height: 1 point; crown spread: 0.75 point
D)circumference: 2 point;s height: 1 point; crown spread: 0.25 point

Answer 2

@nincompoop Just so you know, I actually learned 3D graphing AND some Matrix stuff. :) I guess 14 hours of sleep helped.

Answer 3

THAT is AWESOME! I told you sleep makes the brain fully functional and gives it time to sort things out from when you weren't asleep.

Answer 4

To solve your question, it is always good to make the units consistent. That is to say we need to either make them all in "inches" or "feet." Whichever you decide to use, make sure you have to be consistent throughout.

Answer 5

Wouldn't it be easiest to convert it all to feet?

Answer 6

It would, since most of your units are in feet.

Answer 7

What is my next step?

Answer 8

Converteed into feet: 25.5,15,14

Answer 9

Let points assigned to each inch of circumference be x,
to each foot of height be y and to each foot of crown spread be x.

Then, 306x + 65y + 144z = 407
similarly, 181x + 143y + 96 z = 348
168x + 105y +44z = 248

You have 3 variables 3 equations... solve them to get x,y and z.

Answer 10

wow totally killed it. I was going to point out that we might not need to convert the inch to ft since the point system was according to inch.

Answer 11

so have you done system of equations?

Answer 12

Uhh, no.

Answer 13

I'm not sure how to solve this..

Answer 14

@ziko1995

Answer 15

You can construct a 3 x 3 matrix of the three columns of point data for the three types of trees. The column of total points is not included in the matrix. Is it possible to find the determinant of the matrix?

Answer 16

@nincompoop

Answer 17

@bahrom7893

Answer 18

@satellite73