What's the value of 8j-3k?

Question

If 2/3j-1/4k=5/2, what's the value of 8j-3k?

Answer 1

The fourth law in John Milton Gregory's classic, The Seven Laws of Teaching, is:

Begin with what is already well known to the pupil in the lesson or upon the subject, and proceed to the unknown by single, easy, and natural steps, letting the known explain the unknown.

 

This problem starts with "a given":

     2/3j-1/4k=5/2

 

Proceeding in understandable steps, let's move toward the desired  8j-3k:

   2/3j-1/4k=5/2

   8j - 3k = (5/2)*12     [multiply both sides by the LCM of 3,4, and 3, which is 12]

   8j - 3k = 30

Answer 2

Consider that 12(2/3 j - 1/4 k) = 8j - 3k

 

Therefore, this also equals 12 (5/2) = 60/2 = 30