A person plans to invest up to $10,000 in two different interest-bearing accounts, account X and account Y. Account Y is to contain at least $ $1000$ . Moreover, account X should have at least twice the amount in account Y. Graph the system of linear inequalities describing the various amounts that can be deposited in each account.

Question

Quizplus · Accepted Answer

We can represent the amount invested in Account Y as $y$ and the amount invested in Account X as $x$. Then we have two constraints:
$$y \geq 1000$$
$$x \geq 2y$$
We also know that the total amount invested cannot exceed $10,000$, so we have the constraint:
$$x+y \leq 10,000$$
Graphing these on a coordinate plane, we get a shaded feasible region (bounded by the three lines). Only option B correctly represents this feasible region.

A Person Plans to Invest Up to $10,000 in Two 100010001000

A Person Plans to Invest Up to $10,000 in Two $1000$