Solve the problem.
-Yearly 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 1992. In what year will the sales first be less than
$35,000?
A) 1996
B) 1995
C) 1990
D) 1989

Question

Quizplus · Accepted Answer

To find the year when sales first drop below $35,000, we need to solve for x in the equation $y = 85 - 13.254x < 35$. Converting $35,000 to thousands gives us 35. So, we solve $85 - 13.254x < 35$. Subtracting 85 from both sides gives $-13.254x < -50$. Dividing by -13.254 (and remembering to flip the inequality because we're dividing by a negative number) gives $x > 3.77$. Since x represents years after 1992, and we're looking for the first year sales drop below $35,000, we take the next whole number after 3.77, which is 4. Adding this to 1992 gives 1996. However, since we're looking for the first year it drops below $35,000, and the calculation shows it happens sometime during the fourth year after 1992, the first full year it would be below $35,000 is 1996.

Solve the Problem. -Yearly Sales at a Certain Department Store Follow the Model