Is there any thing like total ratio?

[chijioke]

John is 18 years old and Peter is 24 years old. If they are to share 14 pencils in the ratio of their ages, how many pencils will each receive?
This is how I choose to solve it?
$$John: Peter\\18 : 24$$Ratio of their their ages is
$$J:P\\3:4$$Total ratio is $$3+4=7$$John receives $$\frac{14}{7}×3=6~\text{pencils}$$Peter receives $$\frac{14}{7}×4=8~\text{pencils}$$My question is; is it right to referred $$3+4=7$$ as total ratio? Or is there a better name for it? Please I want to know. And if there is a better name for it, what could it be?

 

[Otis]

is it right to [call the equation 3+4=7 a] total ratio?

Hi chijioke. I don't think I've seen that, before. I just tried searching for a "total ratio" definition in mathematics, but the results I found all contain adjectives (eg: total dependency ratio, total expense ratio). Can you state in more detail what you're thinking when you say "total ratio"?

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BTW, here's another way to approach the exercise.

Age ratio: 18/24 = 3/4

Let A = John's pencil count
Let B = Peter's pencil count

14 pencils total and the proportion A/B=3/4 yield the following system of two equations.

4A – 3B = 00
4A + 3B = 14


$\;$

 

[Dr.Peterson]

My question is; is it right to referred $$3+4=7$$ as total ratio? Or is there a better name for it? Please I want to know. And if there is a better name for it, what could it be?

I would call your 3+4 the "sum of the terms of the ratio"; it might be described as the "total number of parts", or, in some contexts, the "whole".

I certainly wouldn't call it the "total ratio", because in itself, it is not a ratio at all!

 

[chijioke]

X

I would call your 3+4 the "sum of the terms of the ratio"; it might be described as the "total number of parts", or, in some contexts, the "whole".

Let me add, can it also be called total number of proportional parts?

I certainly wouldn't call it the "total ratio", because in itself, it is not a ratio at all!

You are right.