The distance between two islands on the map is 210 miles. A ruler measures this distance as 3.5 inches. How many miles are represented by 1 3/4 inches on the map?

The 'scale' of the map is a ratio (or a fraction).
It's (length on the map) / (distance in the real world) .
Different maps have different scales, but the scale is normally the same everywhere on the same map. So no matter where it is on the map, or ***how ***
long the distance is on the map, the ratio is always the same number on that map .
On this particular map in this question, the ratio is (3.5 inches) / (210 miles) . Any other measurement on the same map has the same ratio ... and what do you have when you have equal ratios ?? That's right ! A proportion ! !
The other measurement has the ratio (1.75 inches) / (X miles) , and THAT fraction is equal to the other one.
(1.75) / ( X ) = (3.5) / (210)
Cross-multiply in the proportion: (1.75 times 210) = (3.5 times X) .
Can you find 'X' now ?
Hint: Divide both sides of that equation by 3.5 .

Answered by AL2006 | 2024-06-10

3.5 210 ​ = 1.75 x ​ 3.5 x = 210 ∗ 1.75 3.5 x = 367.5 x = 105

Answered by Cgordy982 | 2024-06-10

The distance represented by 1.75 inches on the map is 105 miles. This was calculated using the scale established from the map's measurements, given as 3.5 inches corresponding to 210 miles. By setting up a proportion and solving for the unknown distance, we found the answer.
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Answered by AL2006 | 2025-02-16