You plan to invest up to $60,000 in two different interest-bearing accounts. Each account is to contain at least $8000. Moreover, one account should have at least three times the amount that is in the other account. Find a system of inequalities that describes the amount that you can invest in each account.
A) $\left\{ \begin{aligned}
x + y & \leq 60,000 \
x & \geq 8000 \
y & \geq 8000 \
x - 3 y & \leq 0
\end{aligned} \right.$
B) $\left\{ \begin{aligned}
x + y & \geq 60,000 \
x & \geq 8000 \
y & \geq 8000 \
x - 3 y & \leq 0
\end{aligned} \right.$
C) $\left\{ \begin{aligned}
x + y & \geq 60,000 \
x & \leq 8000 \
y & \leq 8000 \
x - 3 y & \geq 0
\end{aligned} \right.$
D) $\left\{ \begin{aligned}
x + y & \leq 60,000 \
x & \geq 8000 \
y & \geq 8000 \
x - 3 y & \geq 0
\end{aligned} \right.$
E) $\left\{ \begin{aligned}
x + y & \geq 60,000 \
x & \geq 8000 \
y & \geq 8000 \
x - 3 y & \geq 0
\end{aligned} \right.$

Question

Quizplus · Accepted Answer

The total investment is up to $60,000, so $x + y \leq 60,000$. Each account must have at least $8000, so $x \geq 8000$ and $y \geq 8000$. One account must have at least three times the amount in the other, which can be represented as $x \geq 3y$ or $y \geq 3x$. Since the inequality $x - 3y \geq 0$ represents $x \geq 3y$, it correctly models the requirement.

You Plan to Invest Up to $60,000 in Two Different {x+y≤60,000x≥8000y≥8000x−3y≤0\left\{ \begin{aligned}x + y & \leq 60,000 \\x & \geq 8000 \\y & \geq 8000 \\x - 3 y & \leq 0\end{aligned} \right.⎩⎨⎧​x+yxyx−3y​≤60,000≥8000≥8000≤0​

You Plan to Invest Up to $60,000 in Two Different $\left\{ \begin{aligned}x + y & \leq 60,000 \\x & \geq 8000 \\y & \geq 8000 \\x - 3 y & \leq 0\end{aligned} \right.$