3. New lights are being installed around the outside of a ferris wheel. If lights cost \( \$ 0.75 \) per foot, the total cost will be \( \$ 164.93 \)

To find the total length of lights installed around the ferris wheel, we can use the information given about the cost of the lights and their price per foot. ### Known Conditions: - Cost per foot of lights: \( c = 0.75 \) - Total cost of lights: \( C = 164.93 \) ### Step-by-Step Solution: 1. **Set up the equation for total cost**: The total cost \( C \) can be expressed as the product of the cost per foot \( c \) and the total length of lights \( L \): \[ C = c \times L \] 2. **Substitute the known values into the equation**: \[ 164.93 = 0.75 \times L \] 3. **Solve for \( L \)**: To find \( L \), we can rearrange the equation: \[ L = \frac{C}{c} = \frac{164.93}{0.75} \] Now, let's calculate \( L \). Calculate the value by following steps: - step0: Calculate: \(\frac{164.93}{0.75}\) - step1: Convert the expressions: \(\frac{\frac{16493}{100}}{\frac{3}{4}}\) - step2: Multiply by the reciprocal: \(\frac{16493}{100}\times \frac{4}{3}\) - step3: Reduce the numbers: \(\frac{16493}{25}\times \frac{1}{3}\) - step4: Multiply the fractions: \(\frac{16493}{25\times 3}\) - step5: Multiply: \(\frac{16493}{75}\) The calculation gives us the total length of lights \( L \) as follows: \[ L = \frac{164.93}{0.75} \approx 219.90\dot{6} \text{ feet} \] ### Final Answer: The total length of lights installed around the ferris wheel is approximately \( 219.91 \) feet.