math 1012 college question 1

Question

The scale on a map is drawn so that  inches corresponds to an actual distance of  miles. If two cities are  inches apart on the map, how many miles apart are they? (Round to the nearest tenth)

Answer 1

This is a question all about using proportions. For example, if a recipe calls for 1 cup of water to make 8 muffins, how many cups should you use to make 4 muffins?

So we set up the following ratio in the original question. We have a scale of 6.5 inches is equal to 325 miles. So that's our ratio:

6.5 in. : 325 mi.

Or 6.5in / 325mi. Let's use the division since it makes the math a bit clearer.

Now we are using this scale, and trying to find a different value. So we set up that ratio.

13.25 in. : x

Again, you can also think of it as 13.25in. / x

We must remember these are ratios, using the same scale. So 6.5 in. / 325 mi. = 13.25in. / x

Now we can solve for x in this equation.

1. Multiply both sides by x: x * 6.5 in. / 325 mi. = 13.25 in.
2. Divide by the fraction in front of x: x = 13.25 in. * 325 mi. / 6.5 in.
3. Cross off your units and use your calculator to do the mult. and division: x = 662.5 mi.
4. Think about your answer, does 662.5mi. make sense? Well if you think about it, 13.25 in. is roughly twice as big as 6.5 in. which we were given as the original scale. So we expect our answer to be roughly twice the size of 325mi. And 662.5mi. is roughly twice the size of 325 mi. (650 mi, is exactly 2 * 325 mi.)