Jack is 12 and his sister Sophia is 16. Jack says that the relationship between his age and Sophia's is proportional and the constant of the proportionality is 12/16 do you agree

No, it is not correct.

Step-by-step explanation:

∵ Jack's age = 12,

And, Sophia's age = 16,

So, the Sophia's age - Jack's age = 16 - 12 = 4,

If x represents the age of jack and y represents the age of Sofia,

Then y - x = 4

⇒ y = 4 + x

Which is equation of a line,

Since, if a line that shows the relation between two variable passes through the origin then the relation is proportional otherwise not,

0 = 4 + 0 (False),

That is, line y = 4 + x does not represents a proportional relation.

Hence, there is no proportional relation between his age and Sophia's is proportional.

Given that current age of Jack = 12 years

Given that current age of Sophia = 16 years

Jack says that the relationship between his age and Sophia's is proportional

If Jack's age is represented by y and Sophia's age by x then we can write y=kx as they are in proportion

where k is called constant of proportion

Now let's plug given ages of each that is y=12 and x=16 into y=kx to find the constant of proportionality

12=k*16

12/16=k

Which is same as the given value of constant of proportionality.

Hence Jack is right about his statement.

But if you think about practical life situation then age of both will not be in proportion

For example after 1 year Jack's age will be 13 and Sophiy's age will be 17

then constant of proportionality using new values will be 13/17

Clearly 12/16 and 13/17 are not same.

So in practical life, age of both will not in in proportion.