In 2003 Acme Computer priced its computers

[JustinM52]

I recognize that this post is a bit stale, so I apologize if I'm dragging it up.

I read through the explanations and I still cannot quite grasp the intuition. I can clearly see that different absolute amounts in each 6 month period produce a different ratio of overall sales for the year, but there is still something that I do not quite get (still).

My immediate response (incorrect response) was to write out that:

First 6 months: Qc/Qp = 3x/2x
Second 6 months: Qc/Qp = 2y/1y

Then, as others did, I averaged them because the variables cancel before you find a common denominator. Regardless of what these unknown multipliers are, both of them cancel before you try and find the overall Qc/Qp for the entire year.

Ultimately you are looking for 5*(Qc/Qp) and with the variable cancellation I felt like I had an isolated ratio for Qc/Qp. My thought was that it isn't necessary to know what the actual values of Qc and Qp are.

I sense that there is something pretty fundamental about ratios and proportions that I am overlooking here, so any help out be great.

Thanks!

[RonPurewal]

with that approach, the overall ratio of computers to printers would be (3x + 2y)/(2x + y) -- an expression in which the variables most certainly DO NOT "cancel" (this is essentially a weighted average, with the multipliers as "weights").