Question

A state park has two pools. The olympic size pool holds 8.12 x 10^(5) gallons of water and the smaller pool holds 5.27 x 10^(5) gallons of water. What is the combined capacity of the pools?

Responses:
A 1.339 x 10^(4) gallons
B 1.339 x 10^(6) gallons
C 13.39 x 10^(10) gallons
D 1.339 x 10^(10) gallons
E 2.85 x 10^(5) gallons

Answer 1

To find the combined capacity of the two pools, we need to add their capacities together:

1. The capacity of the olympic size pool: \( 8.12 \times 10^5 \) gallons
2. The capacity of the smaller pool: \( 5.27 \times 10^5 \) gallons

Now, we add these two numbers together:

\[
8.12 \times 10^5 + 5.27 \times 10^5 = (8.12 + 5.27) \times 10^5
\]

Calculating \( 8.12 + 5.27 \):

\[
8.12 + 5.27 = 13.39
\]

Now, we combine this with the common power of ten:

\[
13.39 \times 10^5
\]

Now we check the format of the answer choices. We can express \( 13.39 \times 10^5 \) in scientific notation by rewriting it:

\[
13.39 \times 10^5 = 1.339 \times 10^6
\]

Thus, the combined capacity of the pools is:

\[
1.339 \times 10^6 \text{ gallons}
\]

So, the correct answer is:

**B 1.339 x 10^(6) gallons**