Find the unknown in the proportion. 5280 feet divided by 1 mile equals 6600 feet divided by an empty box. A. 0.25 mile B. 0.8 mile C. 1.25 miles D. 1,320 miles
The correct answer and explanation is:
The correct answer is C. 1.25 miles.
First, set up the proportion as an equation: 5280 ft1 mile=6600 ftx miles\frac{5280 \text{ ft}}{1 \text{ mile}} = \frac{6600 \text{ ft}}{x \text{ miles}}
This states that 5280 feet is equal to 1 mile, and 6600 feet is equal to some unknown number of miles. To find the value of the unknown, cross-multiply: 5280×x=6600×15280 \times x = 6600 \times 1
So, 5280x=66005280x = 6600
Divide both sides by 5280 to solve for xx: x=66005280=1.25x = \frac{6600}{5280} = 1.25
So the unknown value is 1.25 miles.
Understanding proportions like this is useful for converting between units or comparing quantities that have a constant relationship. In this example, the relationship is the length in feet compared to the length in miles. The standard fact that 1 mile equals 5280 feet allows direct conversion between feet and miles by multiplying or dividing by 5280. Proportions work by equating two ratios that have the same value. Cross-multiplication is the standard method for solving such problems.
Using proportions is common in everyday tasks like converting measurements in recipes, calculating distances on maps, or converting units in science problems. The key is to make sure the units match across the ratios so that the comparison is valid. In this example, feet are compared to miles in both ratios, so the relationship holds true. Solving for the unknown gives the equivalent distance in miles when the distance in feet is known.
Therefore, the empty box should contain 1.25 miles, so the correct choice is C.