Final answer:
To find out how many kilometers are represented by 6.4 centimeters on a map, set up the proportion 3 cm/75 km = 6.4 cm/x km, cross-multiply, and solve for x, yielding 160 kilometers as the actual distance.
Step-by-step explanation:
Determining how many kilometers of actual distance is represented by 6.4 centimeters on a map, given that 3 centimeters represents 75 kilometers. To solve this, we set up a proportional relationship and solve for the unknown distance. First, we write the ratio as 3 cm/75 km and then set it equal to the new ratio of 6.4 cm/x km, where x represents the unknown distance in kilometers. The proportion is: 3/75 = 6.4/x. To find x, we cross-multiply and solve for x: 3x = 6.4 * 75. Then we divide both sides by 3 to get the value of x, which is 160 kilometers. Therefore, 6.4 centimeters on the map represents 160 kilometers in actual distance.