Drawing to Scale, Part 1

Scale drawings save us lots of time and money, but require a bit of math. Here's a sample drawing of a kitchen, with breakfast room and laundry.

Your reaction is likely to be, It's too small! Can we have another?
OK, here's another drawing.

Now you say, It's too big! We've zoomed in too far! 
 Trying one more time - this one is just about right:

Obviously this is not a full-size drawing, because that would be too big to use. We use the concept of scaling to produce an optimally-sized, smaller drawing - big enough to see, handy to print, etc.

This concept of scaling is simple, but gets complicated very quickly. If you know about image types, you can see I made these from a vector drawing program that is designed to scale things up and down. A raster image program spreads pixels apart and the image deteriorates when you zoom in and out.

Now here's the math question:

Q1. Can you tell what scale we have drawn this kitchen?

A1. No and yes. 

I cannot tell just from looking at it on the screen. Some dimensions are shown on it, so I can imagine what the real room is like.

In the center drawing, the TRAYS space is labeled 12. I presume that means the space will be 12 inches wide "in the real world".

In the bottom drawing the breakfast table is marked 36 x 48, so it's 3 feet by 4 feet. I can imagine this because I have eaten breakfast at tables that seat 4 people. But I can't tell the scale yet because I don't know the size of the drawing in the real world.

How can I get a better idea of the size of this? Here's another version. Does it add anything?

Yes, this helps because I have printed the drawing out on a 8 1/2 x 11" sheet of paper. (Trust me, I printed it at its actual size.) We can now compare the actual drawing to a known dimension.

Now I have taped my transparent ruler onto the drawing, over the table. The 48" dimension is equal to 1.5" on the ruler. The drawing scale is 1.5 divided by 48 which can be simplified to 1:32.

Each inch on the drawing is equal to 32 inches in this kitchen.

Another way of describing this scale would be to give the number (or fraction) of inches on the page that equal a foot in the real kitchen.

So if 1 inch = 32 inches, what value X = 12 inches?  Tomorrow we'll give you the answers.