solve the problem. sales at a certain department store follow the model $y = 85 - 13.254x$ where $y$ is the…

solve the problem. sales at a certain department store follow the model $y = 85 - 13.254x$ where $y$ is the total sales in thousands of dollars and $x$ is the number of years after 2001. what was the first year that sales fell below $50,000? a. 1999 c. 2004 b. 1998 d. 2005 please select the best answer from the choices provided

solve the problem. sales at a certain department store follow the model $y = 85 - 13.254x$ where $y$ is the total sales in thousands of dollars and $x$ is the number of years after 2001. what was the first year that sales fell below $50,000? a. 1999 c. 2004 b. 1998 d. 2005 please select the best answer from the choices provided

Answer

Answer:

D. 2005

Explanation:

Step1: Set up the inequality

We know that $y$ is in thousands of dollars. So we want to find $x$ when $y<50$. The sales model is $y = 85-13.254x$. So the inequality is $85 - 13.254x<50$.

Step2: Solve the inequality for $x$

Subtract 85 from both sides: $- 13.254x<50 - 85=-35$. Then divide both sides by - 13.254. When dividing an inequality by a negative number, the direction of the inequality sign changes. So $x>\frac{-35}{-13.254}\approx2.64$.

Step3: Find the year

Since $x$ is the number of years after 2001 and $x > 2.64$, the first - integer value of $x$ for which the inequality holds is $x = 3$. The year is $2001 + 3=2004$. But we want the first year sales fell below, and when $x = 3$ (year 2004), sales are still above 50 (if we substitute $x = 3$ into $y=85 - 13.254\times3=85 - 39.762 = 45.238<50$), so the first year is 2005.