* A certain quantity is measured on two different scales

[ghong14]

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



Hi I have been going through this problem left and right and has not seem to find a way to write the equation that will fit the problem. Can anyone give some pointers and give the steps on how to work this one out.

[RonPurewal]

hi,
please read the forum rules before posting. you must TYPE OUT THE PROBLEM in its entirety, including answer choices. This rule exists not only to reduce the page loading time for our users, but also to make the problems searchable (obviously no one will be able to find this thread if you just post an image of the problem).

please type the problem out in the next few days, or else we will have to delete the thread. thanks.

(also, the graphic is too small to read anyway"”and there doesn't seem to be any obvious way to make it bigger.)

[ghong14]

Thanks Ron, please take a look.

[tim]

Well, you could set up a linear function relating one scale as a function of the other (and I invite you to try!), but perhaps a more intuitive way to do this would be to figure out how much one scale increases relative to the other. Consider:

When R goes from 6 to 24, S goes from 30 to 60. So an 18-point increase in R corresponds to a 30-point increase in S. Putting this in lowest terms, every 5 points that S increases will cause R to increase by 3 points. Since S needs to increase from 60 on up to 100, that's an increase of 40, or eight sets of 5. This corresponds to eight sets of 3 that R will increase above the 24 it was already at. Eight sets of 3 on top of 24 is 8*3+24 = 48.