appy001 wrote:
Two measure standards R and S. 24 and 30 measured with R are 42 and 60 when they are measured with S, respectively. If 100 is acquired with S, what would its value be measured with R?
Please don't paraphrase questions - by not using the actual wording of the question, a LOT gets lost in translation. As written, the question is completely unanswerable.
Also, please provide answer choices, so we can discuss not only pure algebra, but the key alternative strategies that will get you a great score on test day.
Using my magical powers, I'll post the actual question:
Quote:
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
First, we have to understand what "linearly" means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.
From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that R increases, S increases by 5.
We know that S is 100. To get from 60 to 100, we went up by 40, or 8 "jumps" of 5; therefore, R will go up by 8 "jumps" of 3.
24 + 8(3) = 24 + 24 = 48: choose (c).
Note that (a) makes no sense, since if S=60 corresponds to R=24, how could S=100 correspond to a lower value for R?