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.
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.
wronng
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.