Rainbow Mountain in Peru is 5200m in altitude. Given that 1 meter is 3.28 feet, how many feet is the altitude of Rainbow Mountain?

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In order to convert between different units of measurement, we use what is called a conversion factor. A conversion factor is a ratio (written as a fraction) where one of the units is the numerator and one is the denominator. In order to convert one type of unit to another, you will cross-multiply the starting value by the conversion factor. *We decide which unit goes on the top based on what we are trying to convert. Basically, the units have to match - the units of one numerator should be the same as the numerator of the second fraction. In this case, we know the conversion factor to be the number of feet in one meter. This can be written as either of the following: ^{1 m} / _{3.28 ft} OR ^{3.28 ft} / _{1 m} These can both be used as conversion factors because the ratio of feet to meters is the SAME in both. In order to decide which version to use, we come to our problem. We are told that the height of the mountain Is 5200m, and we're trying to convert the meters to feet. Since the number of feet (the height of the mountain in feet) is unknown, we're going to represent It as x. In order to solve using ratios, we need to write the first ratio as a fraction. We know that the height in meters is 5200m, so that will be the numerator in our fraction (ratio) to start. We have decided to use x to represent the unknown number of feet, so our fraction (ratio) will look like this: ^{5200 meters}/_x Now, we know which version of the conversion factor to use. Meters is the unit used in the numerator, so we will use the conversion factor that also has meters in the numerator: ^{1 meter}/_{3.28 feet} Now we can set the ratios equal to one another in preparation to solve. ^{5200 meters}/_x= ^{1 meter}/_{3.28 feet} Now, we can move forward and solve. Cross multiply across the equal sign to eliminate the ratios. This means you multiply the first numerator by the second denominator, and the first denominator by the second numerator. 5200 m • 3.28 ft = x • 1m 17,056m • ft = x • 1m Now, we can see that we have the 1m multiplying the x, so we have to divide both sides by 1m . Note that when you divide, you also divide by the units. This cancels out the m on the left hand side as well. 17,056m • ft ÷ 1m = x • 1m ÷ 1m 17,056 ft = x

Rainbow Mountain in Peru Is 5200m in Altitude