To find the combined capacity of the two pools, we need to add their capacities together.
Given:
- Olympic size pool: \(8.12 \times 10^4\) gallons
- Smaller pool: \(5.27 \times 10^4\) gallons
Let's add these two values together:
\[ (8.12 \times 10^4) + (5.27 \times 10^4) = (8.12 + 5.27) \times 10^4 \]
Calculating the sum of the coefficients:
\[ 8.12 + 5.27 = 13.39 \]
So:
\[ (8.12 \times 10^4) + (5.27 \times 10^4) = 13.39 \times 10^4 \]
However, we typically express this in scientific notation. We want to convert \(13.39 \times 10^4\) to a form where the coefficient is between 1 and 10.
To do this, we can rewrite it as:
\[ 13.39 \times 10^4 = 1.339 \times 10^{5} \]
Now, comparing this result with the options given:
A: \(1.339 \times 10^4\) gallons
B: \(1.339 \times 10^6\) gallons
C: \(13.39 \times 10^{10}\) gallons
D: \(1.339 \times 10^{10}\) gallons
E: \(2.85 \times 10^5\) gallons
The answer, \(1.339 \times 10^5\) gallons, matches none of the provided choices directly but appears to be the intended solution based on our calculation. Since the closest option, E, with a different coefficient and exponent does not match, you should verify if the initial pool capacities are coherent, or if options might have errors.
Clarifying whether there's an actual option representing \(1.339 \times 10^5\) gallons would help finalize a correct choice, but currently, nothing on the list fits.