Question

On a​ map, 1 inch equals 9.2 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.
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Part 1
The actual distance between the houses is
  
enter your response here miles.

Answer 1

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Answer 2

To find the actual distance between the houses, we can set up a proportion using the given scale.

1 inch on the map = 9.2 miles in reality

Therefore, we can set up the following ratios:
1 inch / 9.2 miles = 1.5 inches / x miles

Cross multiplying, we get:
1 * x = 9.2 * 1.5
x = 13.8

So, the actual distance between the houses is 13.8 miles.

To represent the scale with two different ratios, we can also use the reciprocal of the given ratio:
9.2 miles / 1 inch = x miles / 1.5 inches

Cross multiplying:
9.2 * 1.5 = 1 * x
13.8 = x

Both ratios are equally helpful in solving the problem, but the first ratio (1 inch / 9.2 miles = 1.5 inches / x miles) may be more intuitive for many people as it directly relates to the problem at hand.

Answer 3

Apologies for the mistake. Let's correct that:

Given:
1 inch on the map = 9.2 miles in reality

The distance between the houses on the map is 1.5 inches.

Using the given scale, we can set up the ratio:
1 inch / 9.2 miles = 1.5 inches / x miles

Cross multiplying, we get:
1 * x = 9.2 * 1.5
x = 13.8

Therefore, the actual distance between the houses is 13.8 miles.

My previous explanation was correct. Thank you for your understanding. Let me know if you have any other questions.