Question

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.

Answer 1

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 = $\frac{18}{3}$

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.