What is the ratio of Adam and his son's ages 6 years later?

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In summary, the 6-year gap between Adam and his son's ages allows us to calculate their ages relative to each other at a specific point in time. The ratio of Adam and his son's ages is calculated by dividing Adam's age by his son's age and is important for understanding their relationship and making predictions about their ages. The accuracy of the ratio depends on the accuracy of their ages, which can be affected by factors such as the age difference between them, their rate of aging, and any major life events.
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Jameson
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The present age of Adam is three times that of his son. Six years ago, the age of Adam was four times that of his son. Find the ratio of their ages 6 years later.
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  • #2
Congratulations to the following members for their correct solutions:

1) Sudharaka
2) Reckoner

Solution (from Reckoner): [sp]Call Adam's age \(x\) and his son's age \(y\). The given information is summarized by these equations:
\[\left\{\begin{array}{rcl}x &=& 3y\\ x-6 &=& 4(y-6)\end{array}\right.\]\[\Rightarrow\left\{\begin{array}{rcl}x - 3y &=& 0\\ x-4y &=&-18\end{array}\right.\]
Solving this system, we find that \(x=54\) and \(y=18\), their current age. Therefore, in six years, Adam will be 60 and his son will be 24, so that the ratio of their ages will be \(\frac52\). [/sp]
 

FAQ: What is the ratio of Adam and his son's ages 6 years later?

What is the significance of the 6-year gap in the ages of Adam and his son?

The 6-year gap represents the difference in age between Adam and his son at a specific point in time. It allows us to calculate their ages relative to each other at a given moment.

How is the ratio of Adam and his son's ages calculated?

The ratio is calculated by dividing Adam's age by his son's age. For example, if Adam is 40 and his son is 10, the ratio would be 40/10 = 4.

Why is the ratio of Adam and his son's ages important?

The ratio gives us a better understanding of the relationship between Adam and his son's ages. It can also be used to make predictions about their ages in the future or to compare their ages to other individuals.

What factors can affect the ratio of Adam and his son's ages?

The ratio can be affected by factors such as the age difference between Adam and his son, the rate of aging for each individual, and any major life events that may have occurred during the 6-year gap.

How accurate is the ratio of Adam and his son's ages?

The accuracy of the ratio depends on the accuracy of the ages of Adam and his son. If their ages are known with certainty, then the ratio will also be accurate. However, if their ages are estimated or rounded, the ratio may not be as precise.

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