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you are given the total annual interest earned from a total of $12,000 invested in two funds paying the given rates of simple interest. Write and solve a system of equations to find the amount invested at each rate. Annual Interest $500, Rate 1 3% , Rate 2 5%.

Respuesta :

Answer:

The investment at 3% rate = 5000$

The investment at 5% rate = 7000$

Step-by-step explanation:

The following two equations will be developed.

1. x + y = 12000$

2. 3% (x) + 5% (y) = 500$

converting percentage

[tex]3x+5y=50000[/tex]

Solving these two equations will give the answer of x and y.

We will use the substitute method from equation 1

[tex]x+y=12000[/tex]

[tex]x=12000-y[/tex]

Inserting the value in second equation

[tex]3(12000-y)+5y=50000\\36000-3y+5y=50000\\\\2y=50000-36000\\2y=14000\\y=14000/2\\y=7000[/tex]

Now substituting the value of y in Equation 1

[tex]x+y=12000\\x+7000=12000\\x=12000-7000\\x=5000[/tex]

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