Proportions refer to equality. It refers to a comparative relation between certain quantities. To say that there is a proportion between two quantities, there must be a balance. The larger quantity can be expressed in a smaller quantity that must be in exact terms. Proportions have been very useful in making maps, blueprints and other materials for construction. In the problem, in a map, the distance between two cities was found to be 3. 4 inches. The information says that two inches distance in the map is actually 75 miles distance.

With that, we can calculate the actual distance between the two cities to be 127. 5 miles. According to the information, 2 inches is to 75 miles, so, if there is 3. 4 inches, there is 127. 5 miles. To calculate, we make the two ratios equal: 2 inches over 75 miles is equal to 3. 4 inches over the unknown quantity. The unknown quantity can be determined by transposition. Problems in proportions are done by, first, determining the ratios. The ratios must be equal with each other.

Problems in proportion include ratios that are not complete or having one value as unknown. The missing value will be calculated by transposing other values. In our problem, the equation is 2 inches over 75 miles is equal to 3. 4 inches over the unknown which we may assign as X. We transpose X to the other side of the equation and so is 2 inches over 75 miles to give X equal to 3. 4 inches multiplied by 75 miles divided by 2 inches. This will give X the value 127. 5 miles. The answer suggests that the actual distance between the two cities is 127. 5 miles.

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