Question

NO LINKS!!

A person plans to invest up to $19000 in two different interest-bearing accounts, account A and account B. Each account must contain at least $4000. The amount in account B should be at least twice the amount in account A. Write and graph a system of inequalities that describes the various amounts that can be deposited in each account. (Use x for the amount in account A and y for the amount in account B.)

Answer 1

Explanation:

Definition of variables:

• Let x be the amount in account A.
• Let y be the amount in account B.

Given information:

• A total maximum of $19000 deposited in the two accounts.
• Each account must contain at least $4000.
• The amount in account B should be at least twice the amount in account A.

Create a system of inequalities from the given information and defined variables:

• x + y ≤ 19000
• x ≥ 4000
• y ≥ 4000
• y ≥ 2x

When graphing inequalities:

• < or > : dashed line.
• ≤ or ≥ : solid line.
• < or ≤ : shade under the line.
• > or ≥ : shade above the line.

To graph the system of inequalities:

• Draw a solid line at y = -x + 19000 and shade below the line.
• Draw a solid line at x = 4000 and to the right of the line.
• Draw a solid line at y = 4000 and shade above the line.
• Draw a solid line at y = 2x and shade above the line.

The solutions to the system of inequalities are contained in the overlapped shaded region.