Question

Megan has two different maps of California and each of those maps has a different scale. The scale on the first map is 1cm to 10 km. The distance from Los Angeles to Merced is 40 cm. The scale on the second map is 1 cm to 50 km. What is the distance from Los Angeles to Merced on the second map? Explain your reasoning.

Answer 1

The distance from Los Angeles to Merced on the second map is 8 cm. To explain the reasoning, we can use the following steps:

• Find the actual distance from Los Angeles to Merced using the scale on the first map. Since the scale is 1 cm to 10 km, we can multiply 40 cm by 10 km to get 400 km.
• Find the ratio of the scales on the two maps. Since the scale on the second map is 1 cm to 50 km, we can divide 50 km by 10 km to get 5. This means that the second map is 5 times smaller than the first map.
• Find the distance from Los Angeles to Merced on the second map using the ratio of the scales. Since the second map is 5 times smaller than the first map, we can divide 40 cm by 5 to get 8 cm. This is the distance on the second map.