A map measuring 8" x 10" and drawn to the scale 1" = 50 miles is pasted on a sheet of paper of the same size. Find theleast number of sheets of this paper that would have to be taped together to hold this same map if it were drawn to the scale 2" = 25 miles.
a. 2
b. 3
c. 4
d. 8
e. 16
please answer and explain
1" = 50 miles IS 2" = 100 miles
so
if 2" is only 25 miles, we will need four times as long a sheet of paper.
so 4
To find the answer to this question, we need to calculate the total area of the map at the new scale and compare it to the area of a single sheet of paper.
First, let's find the total area of the map at the new scale of 2" = 25 miles. The original map is 8" x 10", so we need to convert it to the new scale:
- The original scale is 1" = 50 miles.
- The new scale is 2" = 25 miles.
To convert from the original scale to the new scale, we divide the distance on the original map by the scale ratio:
- For the height: (10" / 1) x (25 miles / 50 miles) = 5 inches
- For the width: (8" / 1) x (25 miles / 50 miles) = 4 inches
Now that we have the dimensions of the map at the new scale, we can calculate its area:
Area = Height x Width
= 5 inches x 4 inches
= 20 square inches
Next, let's calculate the area of a single sheet of paper, which is also 8" x 10":
Area = Height x Width
= 8 inches x 10 inches
= 80 square inches
Now, we can determine the least number of sheets of paper that would need to be taped together. We divide the total area of the map at the new scale by the area of a single sheet of paper:
Number of sheets = Total area of the map / Area of a single sheet of paper
= 20 square inches / 80 square inches
= 0.25
Since 0.25 is less than 1, we still need at least one whole sheet of paper to hold the map.
Therefore, the least number of sheets of paper that would have to be taped together is 1, which corresponds to option "a."