# Geometry-Ratios homework problem

1. Feb 25, 2004

### Dagenais

I know it is an easy problem, but I want to know if I have the answer correct.

I'm confused whether the answer is already in inches, or is still in feet.

The story problem is:

The larget submarines in the United States Navy are of the Ohio class. Each submarine is 560 feet long.

You purcahse a scale model of one of the submarines. The package states the scale of 1 inch: 16 feet. What is the length of the completed model?

So to solve, I put:

x/560ft = 1/16ft

x=35

OR is x = 420 inches? Is 35 already in inches, or is it still feet and needs to be converted (which results in 420 inches).

2. Feb 25, 2004

### Hurkyl

Staff Emeritus
Well, if you put the units on all of the terms that went into that ratio, your answer would have the units on it!

3. Feb 25, 2004

### Dagenais

I did, and it is 1inch/16ft and xinches/560feet.

Doesn't help much, since I have both inches and feet.

4. Feb 25, 2004

### Hurkyl

Staff Emeritus
Is "x" supposed to be "length of the model" or "number of inches in the length of the model"? (The way you wrote the ratio, it's the latter)

Why doesn't it help? Surely you can do some sort of canceling, or if not, make some sort of substitution...

5. Feb 25, 2004

### Dagenais

So I was right, 35 inches is the answer?

6. Feb 25, 2004

### Integral

Staff Emeritus
You have
$$\frac {1 inch} {16 ft} = \frac {x inches} {560 ft}$$

when you multiply both sides by 560ft you get

$${x inches} = \frac {1 inch * 560 ft} {16 ft}$$

the feet cancel leaving only inches.

7. Feb 25, 2004

### Dagenais

I did it on my calculator.

I completely missed that whole 2nd step. I kind of just typed in the equation in my calculator.

So 35 is right, thanks!

BTW, how did you write those equations? I recall instructions about it on the forums, before new forums were added but I can't find them.

8. Feb 25, 2004

### Integral

Staff Emeritus
click on the formulas to see the text entered to create them.

note that color does not matter.

9. Feb 25, 2004

### Hurkyl

Staff Emeritus
P.S. IMHO, it makes it easier to understand things like this if you solve the problem by first defining your variable x as "The length of the completed model"

Then the ratio is

1 in / 16 ft = x / 560 ft

And when you solve, you're left with

x = 35 in