# Math Help - Finding missiing distances

1. ## Finding missiing distances

5 centimeters= 2 kilometers. I have 5.6 km as the actual distance. How many centimeters would that be?

2. 5 cm = 2 km?. I don't think so. Are you asking how many cm are in 5.6 km?.

What's nice about the metric system is that it's all based on multiples of 10.

There are 100 cm in 1 m and there are 1000 m in 1 km, so how many cm are in 5.6 km?.

EDIT: I am sorry, I see what you mean. It's a scale like what may be on blueprints.

In that event, divide 2 into 5.6 and then multiply by 5.

3. No. This is a hypothetical question given to me. It's saying "If 5cm equals 2km then how many cm's are there in 5.6 km?"

4. I know. Note that I emended my post.

It's just a proportion problem.

$\frac{5}{2}=\frac{x}{5.6}$

Solve for x.

5. So, the cm's would be 2.8? Thank you so much.

6. No, it is not 2.8.

Does that make sense?. If 5 cm = 2 km, then 5.6 km would certainly be more than 2.8 cm.

7. But I multiplied 2.8 and 2, and came up with 5.6.

8. Galactus told you how to do it. :O Just use a ratio:

$\frac{5\ \text{cm}}{2\ \text{km}} = \frac{x\ \text{cm}}{5.6\ \text{km}}$

Note the km units cancel here. Cross multiply now and find x:

$x = \frac{5}{2} \cdot 5.6 = ?\ \text{cm}$

9. Ok, so I multiply 5.6 and 2? Or do I multiply it with both 5 and 2?

Think of this as a variation problem. If y varies directly as x, then:

y = kx

Where k is a constant number.

We have a similar situation here. Let y be the value in centimeters, and x be the value in kilometers. Then, there is a constant k such that:

$5 = 2k$

$k = \frac{5}{2}$

Let's replace k in the first equation:

$y = \frac{5}{2}x$

So, if I want to find how many ? kilometers in centimeters, I plug in the value in km for x and find y.

$y = \frac{5}{2} \cdot 5.6 = 14\ \text{cm}$

11. Ohhhh,ok thanks a lot to both of you.