SOLUTION: please help me....... two school buildings are 7 inches apart on a city map. if the map scale is 4 inches to 3 miles, find the actual distance between the buildings.

Question 511668: please help me.......
two school buildings are 7 inches apart on a city map. if the map scale is 4 inches to 3 miles, find the actual distance between the buildings.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
This problem can be done using a proportion. A proportion is an equality between two ratios.
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It might help you to read this problem as "4 inches is to 3 miles as 7 inches is to X miles."
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Then you can set up two ratios. The first ratio is . Note that the inches are in the numerator and the miles are in the denominator. For the second ratio you need to arrange it so the numerator also has the same units as the numerator of the first ratio. Also the denominator has to have the same units as the denominator of the first ratio. Therefore, this second ratio has to have the inches in the numerator and the miles in the denominator. This second ratio is . The X in the denominator represents the unknown miles you have been asked to find.
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Next you form the proportion by setting these two ratios equal as follows. (I left the dimensions out of the equation to reduce the notation.)
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A simple way to solve proportions involves cross-multiplying. Multiply the each of the numerators by the denominator from the other side of the equation. For this problem multiply the numerator 4 by the denominator X. The result is . Then multiply the numerator 7 times the denominator 3. This result is . (Note that if you draw a line connecting the 4 and the X and another line connection the 7 and the 3, the two lines cross through the equal sign of the proportion. This is why they are called cross-products and the process is called cross-multiplying.)
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Next, set the two cross-products equal as follows:
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Solve for the unknown miles (X) by dividing both sides of this equation by 4 to get:
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When you do the division of the right side you get the answer:
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So the answer you are looking for is miles.
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This means that on a map that is scaled 4 inches to 3 miles, a map measurement of 7 inches represents miles.
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Hope this helps you to understand how proportions can be used to solve problems such as this one.

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