A certain quantity is measured on two different scales, the T-scale and the S-scale, that are related linearly. Measurements on the T-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the T-scale corresponds to a measurement of 100 on the S-scale? Choices
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 T 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, T will go up by 8 jumps of 3.   24 + 8(3) = 24 + 24= 
<gadget id="calculator">24 + 24</gadget>
<output>48</output>
48=48
<result>C</result>
A certain quantity is measured on two different scales, the T-scale and the S-scale, that are related linearly. Measurements on the T-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the T-scale corresponds to a measurement of 100 on the S-scale?