Ratio of Chen and Father's age: How old is Miss Chen's father now?

[Johnx1]

The ratio of Miss Chen's age to her father's age is 2:5. In 8 years' time, the ratio of their ages will become 1:2. How old is Miss Chen's father now?

My work.

Age of Chen = C
Age of Father = F

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Method 1:

Now: (C/F) = (2/5) => C = (2/5)F

After: (C + 8)/(F + 8) = (1/2)

=> C = (F/2 - 4)

* I then plugged C = (2/5)F into C = (F/2 - 4)

=> (2/5)F = (F/2) - 4

Answer: The father age is 40.
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Method 2: I'm trying this other method that I'm not fully sure about call units (not fully sure what's it called)

My work:

Now:
C : F Total
2 : 5 7After:
C : F Total
1 : 2 3So then I made the total units the same. So I times 3 in the Before unit and 7 in the after unit. I got this:

Now:
C : F Total
6 : 15 21

After:
C : F Total
7 : 14 21

Then I found the difference of before and after units. 15 - 14 = 1

so 1 unit = 8 (I chose 8 because it's the difference)

Since we want to know what is age is for now. I did 8 * 5 (the 5 is from the Now ratio) = 40My question is, is what I did for method 1 and 2 correct?

 

[jvicens]

Hello,

Thank you for your response. Your method 1 is correct and is the more common way to solve this type of problem. Your approach in method 2 is also correct, but it is not commonly used and may be more confusing for others to follow. It is important to understand both methods, but method 1 is the more widely accepted and used method.

In method 1, you correctly set up the equations and solved for the father's age to be 40. In method 2, you used the "unit" approach, which is essentially setting up a proportion between the before and after ratios. This also leads to the same answer of the father's age being 40.

Great job on solving the problem! Keep up the good work.