SOLUTION: A professor gives a test, and the scores range from 40 to 80. The professor decides to scale the test in order to make the scores range from 60 to 90. Let "x" represent an origin

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A professor gives a test, and the scores range from 40 to 80. The professor decides to scale the test in order to make the scores range from 60 to 90. Let "x" represent an origin      Log On


   

Question 7003: A professor gives a test, and the scores range from 40 to 80. The professor decides to scale the test in order to make the scores range from 60 to 90. Let "x" represent an original score, and let "y" represent a converted score.

A. Use the ordered pairs (40,60) and (80,90) to write the equation that the professor will use to scale the test scores.
B. What will an original score of 45 become ?
C. If a converted score is 84, what was the original score ?
Answer by glabow(165) About Me  (Show Source):
You can put this solution on YOUR website!
The assumption is that he will scale linearly.
Let y be the new score and x be the old score.
So,
y+=+mx+%2B+b
We can calculate the slope between the two points (40, 60) and (80,90) by
%2890-60%29%2F%2880-40%29=30%2F40=3%2F4
So,
y=%283%2F4%29x+%2B+b
The value of b will be determined substituting one set of values for x and y.
90+=+%283%2F4%2980+%2B+b=60%2Bb
90-60=30=b
The equation of the line which indicates the scaling is
y+=+%283%2F4%29x+%2B+30
Checking:
y=3/4 x 40 + 30 = 30 + 30 = 60 [putting in 40 for x shows y is 60]
y=3/4 x 80 + 30 = 60+30 = 90 [80 converts to 90]
An x=45 would produce what y? [You do it. Hint: I got 63 3/4]
A y=84 would produce what x [You do it]