Scaling : ratio and proportion

[Eabzolid]

Hey guys.
Last question I have is

A scale on a drawing is 1/8" = 3'. Determine the length of a rafter if it measures 1 3/8" on the blueprint.

Thanks

 

[MarkFL]

First, convert both measures to the same units...let's use inches to get a scale of:

\(\displaystyle \frac{1}{8}:36\)

Multiply through by 8:

\(\displaystyle 1:288\)

This means a length of one unit on the blueprint represents 288 of the same unit in the actual building. Can you proceed? Can you find a shortcut rather than use the more general procedure I gave?

 

[Eabzolid]

How did you get those numbers? 36? And 288?

 

[MarkFL]

How did you get those numbers? 36? And 288?

3 ft. is 36 in., and then when multiplying by 8 we get 288. :D

 

[Eabzolid]

Okay. I get the first part.

How do I break down the 1 3/8"? And then solve for both values?

 

[MarkFL]

Okay. I get the first part.

How do I break down the 1 3/8"? And then solve for both values?

I would express it as an improper fraction...that is:

\(\displaystyle \frac{11}{8}\)

Then multiply by 288. Or, you can use the following reasoning:

If 1/8" represents 3' then what must 11/8" represent?

 

[Eabzolid]

I put 11/8= 1.375
1.375x288=396

Do I then convert 396 to inches?

 

[MarkFL]

I put 11/8= 1.375
1.375x288=396

Do I then convert 396 to inches?

That number represents inches...you should convert to feet.

What I was trying to get at before is that if 1/8" equals 3', then 11 times 1/8" must represent 11 times 3' or 33' (which is 396 inches). :D