1. ## Area problem

Suppose that you have a map with a scale of 1 inch= 30 miles. You trace a state on the map, cut out your tracing, and draw this tracing onto card stock. Using a scale, you determine that a full 8 1/2-inch-by-11-inch sheet of cardstock weighs 10 grams. Then you cut out the tracing of the state that is on cardstock and weigh this cardstock tracing. It weighs 5 grams. Approximately what is the area of the state? Explain.

Any help would be appreciated, thanks!

2. So we are given a weight in grams and we need to find the area in(I'm assuming) square miles. Before we can solve this problem we need to come up with a few relationships.

We know: "8 1/2-inch-by-11-inch sheet of cardstock weighs 10 grams"

So: $\displaystyle 8.5in * 11in = 93.5in^2 = 10grams(of cardstock)$

Also we know: "1 inch= 30 miles"

So, by squaring both sides we get: $\displaystyle 1in^2(of cardstock) = 900mi^2$

Also we know we have: 5grams(of cardstock)

Now we have everything we need to solve this problem, it's as simple as multiplying the relationships and canceling out units.

$\displaystyle 5grams(of cardstock) * $$\displaystyle [93.5in^2(of cardstock) / 10grams(of cardstock)] *$$\displaystyle [900mi^2 / 1in^2(of cardstock)]$

You'll see that everything cancels out and you are left with an answer in $\displaystyle mi^2$