Two rival companies began the same year. The equations below model the number of employees, y, at these companies x years after the companies began.

Company R: y = 3x + 24

Company T: y= 4x + 10

Company R stated, “We have 42 employees, the same number of employees as company T has this year.” Determine if company R’s claim is possible. Explain your reasoning.

Company T stated, “After 15 years, we will have the same year of employees as company R.” Determine if company T’s claim is possible. Explain your reasoning.

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 =

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.

the 4th choice is the correct one

step-by-step explanation: