two rival companies began the same year. the equations below model the number of employees, y, at these…

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.\ncompany r: y = 3x + 24\ncompany t: y = 4x + 10\ncompany r stated, \we have 42 employees, the same number of employees as company t has this year.\ determine if company rs claim is possible. explain your reasoning.\ncompany t stated, \after 15 years, we will have the same number of employees as company r.\ determine if company ts claim is possible. explain your reasoning.\nenter your answers and your explanations in the space provided.

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.\ncompany r: y = 3x + 24\ncompany t: y = 4x + 10\ncompany r stated, \we have 42 employees, the same number of employees as company t has this year.\ determine if company rs claim is possible. explain your reasoning.\ncompany t stated, \after 15 years, we will have the same number of employees as company r.\ determine if company ts claim is possible. explain your reasoning.\nenter your answers and your explanations in the space provided.

Answer

Explanation:

Step1: Check Company R's claim

Set $y = 42$ for Company R's equation $y=3x + 24$. Then solve for $x$: $42=3x + 24$. Subtract 24 from both sides: $42-24=3x$, so $18 = 3x$. Divide both sides by 3: $x=\frac{18}{3}=6$. Now check Company T's equation with $x = 6$. Substitute $x = 6$ into $y = 4x+10$, we get $y=4\times6 + 10=24 + 10=34\neq42$. So Company R's claim is not possible.

Step2: Check Company T's claim

Set $x = 15$. For Company R, $y_R=3\times15+24=45 + 24=69$. For Company T, $y_T=4\times15+10=60 + 10=70\neq69$. So Company T's claim is not possible.

Answer:

Company R's claim is not possible because when Company R has 42 employees ($x = 6$), Company T has 34 employees. Company T's claim is not possible because after 15 years, Company R has 69 employees and Company T has 70 employees.