Answer:
Both the claims by the companies are not possible.
Step-by-step explanation:
Equations modeling number of employees 'y' after 'x' years of the start are,
For company R: y = 3x +24
For company T: y = 4x + 10
If Company R states that this year they have 42 employees,
42 = 3x + 24
3x = 42 - 24
x = ![\frac{18}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B3%7D)
x = 6 years
So company has completed 6 years this year.
Now we put x = 6 years in the equation for company T.
y = (4×6) + 10
y = 24 + 10
y = 34
Which doesn't match with the number of employees of the company R.
Therefore, claim of company R is not possible.
Company T stated that after 15 years they will have the same number of employees as company R.
For company T : y = 4(15) + 10
y = 70 employees
For company R : y = 3(15) + 10
y = 45 + 10
y = 55 employees
Therefore, claim of the company T is also not possible.