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? Options
A) 20 B) 36 C) 48 D) 60 E) 84
<gadget id="calculator">24 - 6</gadget>
<output>18</output>

<gadget id="calculator">100 - 60</gadget>
<output>40</output>

<gadget id="calculator">60 - 30</gadget>
<output>30</output>

<gadget id="calculator">40 / 30</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">18 * (4/3)</gadget>
<output>24</output>

<gadget id="calculator">24 + 24</gadget>
<output>48</output>

<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?
add(multiply(subtract(24, 6), divide(subtract(100, 60), subtract(60, 30))), 24)
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 = 48 = c