The place to begin is learning what a proportion actually is.
A proportion is two ratios that are equal.
The map scale gives you one ratio: 1/2 to 4.
Picking a symbol to represent the unknown number of feet (like x) allows you to write another ratio: (2+3/8) to x.
These two ratios are equal, so here is a proportion:
\(\displaystyle \frac{1/2}{4} = \frac{2+3/8}{x}\)
Solve for x.
In the proportion that I wrote above, the units in the numerators are inches and the units in the denominators are feet, yes?
\(\displaystyle \frac{\text{inches}}{\text{feet}} = \frac{\text{inches}}{\text{feet}}\)
Therefore, because x appears on the bottom, its value represents the actual length of the room in feet.
By the way, I chose to write the ratios as inches to feet. If you like, you could write them as feet to inches, instead.
Doing that would make the proportion:
\(\displaystyle \frac{\text{feet}}{\text{inches}} = \frac{\text{feet}}{\text{inches}} \)
\(\displaystyle \frac{4}{1/2} = \frac{x}{2+3/8}\)
The solution for x is the same, in each proportion, so you can choose to solve either one.
If you need more help, please ask specific questions about the parts you don't understand or show some work. :cool:
