Question

a swim race has a total distance of 22.5 mi. race officials want to mark the course every 600 yd with a buoy, including one at the finish line. (the starting line does not need a buoy.) how many buoys are needed?
first fill in the blanks on the left side of the equation using three of the ratios shown. then write your answer on the right side of the equation.
ratios:
\\(\frac{3 \text{ft}}{1 \text{yd}}\\)
\\(\frac{1 \text{yd}}{3 \text{ft}}\\)
\\(\frac{600 \text{yd}}{1 \text{buoy}}\\)
\\(\frac{1 \text{buoy}}{600 \text{yd}}\\)
\\(\frac{5280 \text{ft}}{1 \text{mi}}\\)
\\(\frac{1 \text{mi}}{5280 \text{ft}}\\)
\\(\frac{22.5 \text{mi}}{1}\\) \\(\times\\) \\(square\\) \\(\times\\) \\(square\\) \\(\times\\) \\(square\\) \\(=\\) \\(square\\) buoys

Explanation:

Step1: Convert miles to feet

$\frac{22.5\ \text{mi}}{1} \times \frac{5280\ \text{ft}}{1\ \text{mi}}$

Step2: Convert feet to yards

$\times \frac{1\ \text{yd}}{3\ \text{ft}}$

Step3: Convert yards to number of buoys

$\times \frac{1\ \text{buoy}}{600\ \text{yd}}$

Step4: Calculate the result

First, cancel units: $\text{mi}$ and $\text{ft}$ cancel out, leaving $\text{buoy}$.
Compute the value: $22.5 \times 5280 \times \frac{1}{3} \times \frac{1}{600} = 22.5 \times \frac{5280}{1800} = 22.5 \times 2.933\dot{3} = 66$

Answer:

66 buoys

The completed equation is:
$\frac{22.5\ \text{mi}}{1} \times \frac{5280\ \text{ft}}{1\ \text{mi}} \times \frac{1\ \text{yd}}{3\ \text{ft}} \times \frac{1\ \text{buoy}}{600\ \text{yd}} = 66\ \text{buoys}$