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 $$ \$ 164.93 $$

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UpStudy AI · Accepted Answer

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.
The total length of lights installed around the ferris wheel is approximately 219.91 feet.

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 \( \$ 164.93 \)

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