PS

[ketkoag]

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?
A. 20
B. 36
C. 48
D. 60
E. 84

OA: C

[DanaJ]

The linear relationship between the two scales means that you can use a first degree equation to express it:
a*(S-scale measurement) + b = R-scale measurement.
You are told that:
a*30 + b = 6
a*60 + b = 24.
Subtract the two equations to get that 30a = 18 or that a = 3/5.
This will make b = -12.
So, for S = 100, R will be 3/5 * 100 - 12 = 48.