Suppose that the veterans of the Korean War and the veterans of WWII are mutually exclusive. Together, the veterans of the Korean War and the veterans of WWII, account for X% of the veterans in the United States in 2009. The number of veterans of the Vietnam era is X% + 11.6% in 2009. What is the number of Vietnam era veterans in the United States in 2009? Express your answer to the nearest whole number.
We are told that together, the number of Korean War and WWII veterans in 2009 is X%. Using the information from the previous problem we have X% = 12.4% + 10.7% = 23.1%. That means the number of Vietnam era veterans is 23.1% + 11.6% = 34.7% of the veterans in the United States in 2009. Thus, there were 21,854,374(0.347) = 7,583,467.778 ≈ 7,583,468 veterans of the Vietnam era in the United States in 2009.
To find the number of Vietnam era veterans in the United States in 2009, we need to know the value of X. However, the information given in the question does not provide the value of X directly. We only know that the veterans of the Korean War and the veterans of WWII together account for X% of the veterans in the United States in 2009.
To solve this problem, we will need to consider the fact that the percentages given must add up to 100%. Let's break it down step by step:
1. Let's assume that the total number of veterans in the United States in 2009 is V.
2. According to the information given, the veterans of the Korean War and veterans of WWII together account for X% of the veterans in 2009.
So, the number of veterans from the Korean War and WWII combined would be (X/100) * V.
3. The number of veterans from the Vietnam era is X% + 11.6% of the veterans in 2009.
So, the number of veterans from the Vietnam era would be (X/100) * V + 0.116 * V.
4. The total number of veterans in the United States in 2009 is the sum of the veterans from these three eras:
V = (X/100) * V + (X/100) * V + 0.116 * V.
5. Simplifying the equation:
V = (2X/100) * V + 0.116 * V.
6. We can now solve for V:
V - (2X/100) * V - 0.116 * V = 0.
V * (1 - 2X/100 - 0.116) = 0.
V * (0.884 - 2X/100) = 0.
7. Since V cannot be zero, we have:
0.884 - (2X/100) = 0.
2X/100 = 0.884.
2X = 0.884 * 100.
2X = 88.4.
X = 88.4 / 2.
X = 44.2.
8. Now that we have found the value of X, we can find the number of veterans from the Vietnam era:
Number of Vietnam era veterans = (44.2/100) * V + 0.116 * V.
As we do not have the actual value of V given in the question, we cannot find the exact number of veterans from the Vietnam era. We need to know the value of V in order to calculate it accurately.