Question

An 8-inch by 10-inch map is drawn to a scale of 1 inch = 50 miles. If the same map is to be enlarged so that now 2 inches = 25 miles, how many 8-inch by 10-inch pieces of blank paper will be taped together in order for all of this map to fit?

Answer 1

2500 pieces of blank paper measuring 8 inches by 10 inches would need to be taped together.

Explanation:

To determine how many 8-inch by 10-inch pieces of paper are needed to fit the enlarged map, we need to calculate the dimensions of the enlarged map.

The original map had a scale of 1 inch = 50 miles. Since the map was 8 inches by 10 inches, the actual area it represented was:

8 inches x 50 miles/inch = 400 miles (width)

10 inches x 50 miles/inch = 500 miles (height)

Now, we have a new scale of 2 inches = 25 miles. To find the dimensions of the enlarged map, we can use the ratio of the scales:

2 inches / 1 inch = 25 miles / x miles

Cross-multiplying, we get:

2x = 1 inch x 25 miles

2x = 25 miles

x = 25 miles / 2

x = 12.5 miles

So, the enlarged map will represent an area of 400 miles (width) by 500 miles (height), using the new scale of 2 inches = 25 miles.

To determine how many 8-inch by 10-inch pieces of paper are needed, we divide the dimensions of the enlarged map by the dimensions of each piece of paper:

Number of paper pieces needed = (400 miles / 8 inches) x (500 miles / 10 inches)

Number of paper pieces needed = 50 x 50

Number of paper pieces needed = 2500

Therefore, to fit the entire enlarged map, approximately 2500 pieces of blank paper measuring 8 inches by 10 inches would need to be taped together.