You are reducing a map of dimensions 2 ft by 3 ft to fit to a piece of paper 8 in by 10 in. What are the dimensions of largest possible map that can fit on the page?

I really don't know how to do this but so far I tried to make 2 proportions by changing feet to inches. This is the proprtion:

8/10=24/x and 8/10=120/x. Can you help me?

The answer is 20/3 inches or 6 2/3 inches by 10 inches

2 x 3 feet is 24 x 36 inches. The length dimension (10 inches) will be the limiting dimension on the 8x10 page. The reduction ratio will be 36:10 = 3.6

The width dimension of the map will be 2/3 x 10 = 6.67 inches. There will be blank space along the 8 inch width of the page, since the map will be only 6.67 inches wide.

So the printed map will have dimensions of 10 x 6.67 inches.

WUT?

Of course! I can help you with this problem.

To find the dimensions of the largest possible map that can fit on the page, we need to find the scale factor by which the map needs to be reduced.

You started off correctly by setting up proportions using the given dimensions. However, the proportions you set up are not quite accurate. Let's correct them and solve the problem step by step.

First, we need to convert the dimensions of the original map to inches. Since there are 12 inches in a foot, the original map dimensions are 2 ft x 3 ft, which can be converted to 24 in x 36 in.

Next, we set up the proportion:

original map dimensions / new map dimensions = scale factor

So, we have:

24 in / x = 8 in / 10 in

To solve for x, we cross-multiply and then solve for x:

(24 in) * (10 in) = (8 in) * x

240 in^2 = 8x

Divide both sides of the equation by 8 to isolate x:

240 in^2 / 8 = x

x = 30 in^2

Therefore, the new map dimensions should be 30 in x 30 in to fit within the given paper size of 8 in x 10 in.

huh?