Asked by Nathan Hammon on Mar 10, 2024

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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 $ 100010001000 . 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.

A)  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. A)    B)    C)    D)    E)
B)  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. A)    B)    C)    D)    E)
C)  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. A)    B)    C)    D)    E)
D)  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. A)    B)    C)    D)    E)
E)  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. A)    B)    C)    D)    E)

Linear Inequalities

Mathematical statements that involve linear expressions and inequalities, showing that one side is either greater than, less than, greater than or equal to, or less than or equal to the other.

System

A group of guidelines or processes used to accomplish a task; a systematic strategy or technique.

  • Understand the relationship between quantities and constraints in allocation problems through linear inequalities.
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PK
Pratiksha khatiwoda

Mar 10, 2024

Final Answer :
B
Explanation :
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≥1000y \geq 1000y1000
x≥2yx \geq 2yx2y
We also know that the total amount invested cannot exceed $10,000$, so we have the constraint:
x+y≤10,000x+y \leq 10,000x+y10,000
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.