Determine how many for this many

[Guest]

what is the equation to determine how many I need for 8 when I need 2 for 3?

[HallsofIvy]

That's not a very clearly phrased question! In what sense do you "need 2 for 3"? If you mean that the relation between the two number is a simple addition, so that y= x+ b, then when x= 2, y= 3, 3= 2+ b so b= 1. Then to get 8, you need 8= x+ 1 so x= 7. In this sense, since you "need 2 to get 3", you "need 7 to get 8".

But if the relation is a multiplication, y= ax then 3= 2a so a= 3/2. Then 8= (3/2)x so x= (2/3)8= 16/3= 5 and 1/3. In this sense, since you "need 2 to get 3", you "need 16/3 to get 8".

But there can be many different relations! For example, y= ax^2 is yet another relation between x and y. Here, if you "need 2 to get 3", that is, if x= 2 gives y= 3, 3= a(2)^2= 4a so a= 4/3. Then "to get 8" you would have to have (4/3)x^2= 8 so x^2= (3/4)(8)= 6, x= sqrt(6). In this sense, since you "need 2 to get 3" you "need sqrt(6) to get 8".

It is impossible to give one answer to the question as posted.