14 Denver, Engle and Fldo are all dogs who eat differing amounts of dop food. Benver gets $$ \frac{B}{19} $$ of the dog food. Engle and Fido share the rest of the food in the ratio $$ 9: 5 $$ What is Fido's share of the dog food? Show your answer as a percentage, rounded to the nearest percent if necessay

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To find Fido's share of the dog food, we can follow these steps:

1. **Identify the total amount of dog food**: Let's denote the total amount of dog food as $$ T $$.

2. **Calculate Benver's share**: Benver gets $$ \frac{B}{19} $$ of the dog food. Therefore, his share can be expressed as:
   $$
   \text{Benver's share} = \frac{T}{19}
   $$

3. **Calculate the remaining food for Engle and Fido**: The remaining food after Benver's share is:
   $$
   \text{Remaining food} = T - \frac{T}{19} = T \left(1 - \frac{1}{19}\right) = T \left(\frac{18}{19}\right)
   $$

4. **Share the remaining food between Engle and Fido**: Engle and Fido share the remaining food in the ratio $$ 9:5 $$. Let $$ E $$ be Engle's share and $$ F $$ be Fido's share. We can express their shares as:
   $$
   E + F = \frac{18T}{19}
   $$
   Given the ratio $$ 9:5 $$, we can express $$ E $$ and $$ F $$ in terms of a common variable $$ x $$:
   $$
   E = 9x \quad \text{and} \quad F = 5x
   $$
   Therefore, we have:
   $$
   9x + 5x = \frac{18T}{19}
   $$
   Simplifying this gives:
   $$
   14x = \frac{18T}{19}
   $$

5. **Solve for $$ x $$**:
   $$
   x = \frac{18T}{19 \cdot 14} = \frac{18T}{266}
   $$

6. **Calculate Fido's share**:
   $$
   F = 5x = 5 \cdot \frac{18T}{266} = \frac{90T}{266} = \frac{45T}{133}
   $$

7. **Convert Fido's share to a percentage**:
   To find Fido's share as a percentage of the total dog food $$ T $$:
   $$
   \text{Fido's percentage} = \left(\frac{F}{T}\right) \times 100 = \left(\frac{45T/133}{T}\right) \times 100 = \frac{45}{133} \times 100
   $$

Now, let's calculate this percentage.

I'll perform the calculation now.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{45}{133}\times 100$$
- step1: Multiply:
  $$\frac{45\times 100}{133}$$
- step2: Multiply:
  $$\frac{4500}{133}$$
Fido's share of the dog food as a percentage is approximately $$ 33.83\% $$.

Rounding this to the nearest percent, Fido's share is:

$$
\boxed{34\%}
$$
Fido's share of the dog food is 34%.

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