A certain quantity is measured on two different scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the R-scale corresponds to a measurement of 100 on the S-scale?
This is a neat question! It's a really easy problem you've seen before in disguise.
Because we know these are linearly related, we are basically being told that
S = Rx +b where x is some multiple and b is a constant.
does this look familiar yet? We're basically being given two points on the x/y coordinate plane, being asked to find the equation of the line and a 3rd point on the line.
Let's plug in some values from the conversion we know.
30 = 6x +b
60 = 24x +b
Combine these to get:
30 = 18x
x = 30/18 = 5/3
Then we can solve for b:
30 = 6* (5/3) +b
30 = 10 +b
b = 20
Or by combining the two equations:
120 = 24x + 4b
60 = 24x +b
60 = 3b
b = 20
So the conversion between R and S is as follows:
S = (5/3)R +20
Since we're looking for S=100, let's just throw it in!
100 = (5/3)R + 20
80 = (5/3)R
240/5 = R
R = 48
So the answer is 48!
