Question

Select the correct answerThe manager at a car dealership is tracking the selling prices of two different used car models. When the tracking began, the selling pnce of model A wasless than $8,000, and the selling price of model B was at most $10,000. The manager has determined that the price of model A is decreasing at a rate of12% each year, and the price of model 8 is decreasing at a rate of 154 each year.Which system of inequalities can be used to determine atter how many years, that the selling price y, will be the same for both car models?

Answer 1

Let:

ya = price of model A

yb = price of model B

the selling price of model A was less than $8,000, and the selling price of model B was at most $10,000, so:

`\begin{gathered} ya<8000 \\ yb\le10000 \end{gathered}`

the price of model A is decreasing at a rate of 12% each year, and the price of model B is decreasing at a rate of 15% each year. So:

`\begin{gathered} ya=8000(1-0.12)^t=8000(0.88)^t \\ yb=10000(1-0.15)^t=10000(0.85)^t \\ so\colon \\ \begin{cases}y<8000(0.85)^t \\ y\le10000(0.85)^t\end{cases} \end{gathered}`