给我讲解这道题---Here is the extraction of the content from the image:
**Question 6:**
6. 2012年, 爸爸的年龄是姐姐和妹妹年龄和的 4倍, 2018年, 爸爸的年龄是姐姐和妹妹年龄和的 2 倍, 那么爸爸出生在____年.
**Question 7:**
7.
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Let's analyze this age problem step by step. We have a father and two sisters. In 2012, the father's age was 4 times the sum of the two sisters' ages. By 2018, this ratio changed to 2 times. We need to find when the father was born.
Now let's set up our variables clearly. Let F represent the father's age and S represent the sum of the two sisters' ages. We have two key equations: In 2012, F equals 4 times S. In 2018, F equals 2 times S. These will be our foundation for solving the problem.
Now let's consider the time relationship. From 2012 to 2018, exactly 6 years passed. This means the father's age increased by 6 years. Since there are two sisters, and each sister's age increased by 6 years, the sum of their ages increased by 12 years total.
Now let's solve our system of equations. We have F equals 4 times S in 2012, and F plus 6 equals 2 times S plus 12 in 2018. Substituting the first equation into the second gives us 4S plus 6 equals 2S plus 24. Simplifying: 2S equals 18, so S equals 9. This means the sum of the sisters' ages in 2012 was 9 years.
Now we can find the father's age in 2012. Since the sum of sisters' ages was 9, and the father's age was 4 times that, he was 36 years old in 2012. Therefore, his birth year is 2012 minus 36, which equals 1976. Let's verify: in 2018, the father would be 42 and the sisters' ages would sum to 21. Indeed, 42 equals 2 times 21, confirming our answer is correct.