Question

question 6
in one year, a theme park had approximately $2 \times 10^7$ guests. in the same year, a second theme park had approximately $4 \times 10^6$ guests. which is a true statement about the number of guests each theme park had?
\bigcirc the first theme park had about 2 times as many guests than the first.
\bigcirc the first theme park had about 10 times as many guests as the first.
\bigcirc the second theme park had about 2 times as many guests as the first.
\bigcirc the first theme park had about 5 times as many guests than the second.

Explanation:

Step1: Identify the number of guests for each park

Let the number of guests in the first theme park be \( N_1 = 2\times10^{7} \) and in the second be \( N_2 = 4\times10^{6} \).

Step2: Calculate the ratio of \( N_1 \) to \( N_2 \)

To find how many times \( N_1 \) is of \( N_2 \), we compute \( \frac{N_1}{N_2}=\frac{2\times 10^{7}}{4\times 10^{6}} \).
Simplify the coefficients and the powers of 10 separately: \( \frac{2}{4}=0.5 \) and \( \frac{10^{7}}{10^{6}} = 10^{7 - 6}=10^{1} = 10 \).
Multiply these results: \( 0.5\times10 = 5 \). Wait, no, wait: Wait, \( \frac{2\times10^{7}}{4\times10^{6}}=\frac{2}{4}\times10^{7 - 6}=\frac{1}{2}\times10^{1} = 5 \)? Wait, no, \( 2\times10^{7}=20\times10^{6} \), so \( \frac{20\times10^{6}}{4\times10^{6}}=\frac{20}{4}=5 \). Wait, but the options: Wait, the first park has \( 2\times10^{7}=20,000,000 \), the second has \( 4\times10^{6} = 4,000,000 \). Then \( 20,000,000\div4,000,000 = 5 \). So the first theme park has about 5 times as many guests as the second? Wait, no, the options: Let's check the options again. Wait, the options are:

1. The first theme park had about 2 times than the first. (Wrong wording, maybe "than the second")
2. The first theme park had about 10 times as many as the first. (Nonsense)
3. The second theme park had about 2 times as many as the first. (No, 4e6 vs 2e7: 4e6 is 0.2 of 2e7, so 2e7 is 5 times 4e6)
4. The first theme park had about 5 times as many guests than the second. (Wait, the fourth option: "The first theme park had about 5 times as many guests than the second." Wait, but the calculation is \( 2\times10^{7}\div4\times10^{6}=5 \). So the first has 5 times as many as the second. Wait, but let's re - express the numbers:

\( 2\times10^{7}=20\times10^{6} \)

\( 4\times10^{6}=4\times10^{6} \)

Then \( \frac{20\times10^{6}}{4\times10^{6}} = 5 \). So the first theme park has about 5 times as many guests as the second. Looking at the options, the last option is "The first theme park had about 5 times as many guests than the second." (Even though "than" should be "as", but among the options, this is the correct one in terms of the multiple. Wait, but let's check the options again:

Wait the options are:

• The first theme park had about 2 times as many guests than the first. (Incorrect)
• The first theme park had about 10 times as many as the first. (Incorrect)
• The second theme park had about 2 times as many as the first. (Incorrect, since 4e6 is less than 2e7)
• The first theme park had about 5 times as many guests than the second. (This is the correct multiple, even with the "than" error, it's the only one that matches the calculation \( 2\times10^{7}\div4\times10^{6} = 5 \))

Wait, maybe there was a typo in the options, but based on the calculation, the first park has 5 times the number of guests of the second. So the correct option is the last one: "The first theme park had about 5 times as many guests than the second."

Answer:

The first theme park had about 5 times as many guests than the second. (The option corresponding to this statement, assuming the last option is "The first theme park had about 5 times as many guests than the second.")