On a map, 1 inch equals 7.2 miles. Two houses are 1.5 inches apart on the map. What is the actual distance between the houses? Use pencil and paper. Show how you can represent the scale with two different ratios. What ratio is more helpful for solving the problem? Explain.
To find the actual distance between the houses, we first need to find the scale factor from the map to real life.
Given that on the map, 1 inch equals 7.2 miles, we can set up two ratios to represent the scale:
1 inch / 7.2 miles
x inches / 1.5 inches
To find the scale factor x, we can cross multiply:
1 * 1.5 = 7.2 * x
1.5 = 7.2x
x = 1.5 / 7.2
x = 0.208333...
So, the scale factor is approximately 0.208.
Now, to find the actual distance between the houses, we multiply the distance on the map by the scale factor:
1.5 inches * 0.208 = 0.312 miles
Therefore, the actual distance between the houses is 0.312 miles.
The ratio that is more helpful for solving the problem is the one that directly relates the distances on the map to the actual distances. In this case, the ratio of 1 inch to 7.2 miles is more helpful as it allows us to directly convert the distance on the map to the actual distance.
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I apologize for the mistake in my calculations. Let's correct that.
Given that on the map, 1 inch equals 7.2 miles, we can set up the following ratios:
1 inch / 7.2 miles = 1.5 inches / x miles
To find the actual distance between the houses (x), we can cross multiply:
1 * x = 1.5 * 7.2
x = 10.8 miles
Therefore, the actual distance between the houses is 10.8 miles.
So, the more helpful ratio for solving the problem is using the one that directly relates the distances on the map to the actual distances.