A Chinese Saying

I remember when I was much younger, my father used to keep me quiet in an argument whenever I came out with an unanswerable question or a fact with a ubiquitous statement among oriental families. It goes something like this: "我食鹽多過你食米" which literally means "I ate salt much more than you ate rice". 

It was a figurative statement referring to his experience in life being much more longer and richer than mine gives him a right for authority and I, as a younger generation should learn to respect it. 

There goes a while each time this happens, I would stay quiet and let him have his way. Now, I was curious to find out if that aged-old "dictum" is even theoretically possible. 

So, before we start out with the math, we have to make 4 assumptions to ease the calculations:

1. An average person eats about 200 grams of rice (as one bowl) every-day.

2. An average Asian, start feeding on rice at the age of 5. 

3. My father, a savoury food lover, consume 3 times more salt than the recommended diet by Scientific Advisory Committee Nutrition (SACN) in 2003. 

4. He will start consuming salt in amount stated in assumption (3) since his birth. 

Based on assumption (1) and (2) we say the child would consume 73 kg of rice per year starting at the age of 5. 

The SACN recommended table salt intake per day is 4 grams per day. Following assumption (3) would translate into 4.38 kg of salt per year. 

Now, lets follow this simple timeline diagram, we can conclude an algebraic expression for the age my father have to give birth to me for the time he claimed "我食鹽多過你食米" to be valid. 

Naturally, we can say the collective amount of rice the child ate would be 73n and collective salt intake for father would be 4.38m. From the diagram, we can also see clearly that in terms of years, m=x+5+n. 

For the amount of salt needed to be equal to the amount of rice consumed, we simply equate the two rates of consumption to find the ratio of time:

73n = 4.38m

73n = 4.38(x+5+n)

which simplifies to:

15.67n-5 = x , when n=1, child at 6 years old, n=2, child at 7 years old, ...

Which means, if I were to be 7 years old, having ate two years' worth of rice, my father would have to consume salt for 26 years before bringing me into this world. Sounds perfectly reasonable isn't it? 

Extend that to 3 years more, you will realize this is not possible. Say if he claimed that statement while I was 10 years old, I would have to be born when he is 73 years old for the statement to be valid. 

*  *  *

Truth is, these days he no longer use such statement on me since I was in middle school not because I argued with him using this simple proof; but time itself and the things he had shown to the family are the elements which strengthens the father-and-son bond to such an extend where statement like this becomes irrelevant. 

This post is merely a muse of my childhood, brought back and checked using simple mathematics.