Question

The scale on a map of the moon’s surface indicates that 0.4 inches = 100 miles. Sen wants to know the distance between two large craters. If on the map, the distance between the two craters is 7.4 inches, then what is the actual distance, in miles, between the two craters? A. 74 miles B. 296 miles C. 1,850 miles D. 2,960 miles

Short answer

The actual distance between the two craters is 1,850 miles. The correct answer is C. 1,850 miles.

Step-by-step solution

Set up the proportion

To set up a proportion, we can use the given scale in the problem: 0.4 inches on the map is equal to 100 miles in reality. The unknown distance we want to find is represented by x miles. We can set up the proportion as follows: \(\frac{7.4 \, \text{inches}}{0.4\, \text{inches}} = \frac{x\, \text{miles}}{100 \,\text{miles}}\)

Solve for x

Now, we need to solve the proportion for x. To do this, we can cross-multiply: \(7.4 \, \text{inches} \times 100 \, \text{miles} = 0.4 \, \text{inches} \times x \, \text{miles}\) Next, let's divide both sides by 0.4 inches: \(\frac{7.4\, \text{inches} \times 100 \, \text{miles}}{0.4\, \text{inches}} = x\, \text{miles}\)

Calculate the value for x

Now, we just need to perform the calculation to find the value of x: \(x = \frac{7.4\, \text{inches} \times 100 \, \text{miles}}{0.4\, \text{inches}} = 1,850\, \text{miles}\) So the actual distance between the two craters is 1,850 miles. The correct answer is C. 1,850 miles.