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an amount of money is invested at 3% annual simple interest, & $2000 more than that amount is invested at 4%. The total annual interest is $920. How much is invested at each rate?

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pedrocarratore

Answer:

$12,000 at 3%.

$14,000 at 4%.

Explanation:

Let A be the amount invested at 3%, and B be the amount invested at 4%. The following system of equations can be modeled from the provided information:

[tex]B=A+2,000\\0.03A+0.04B = 920\\[/tex]

Solving the linear system:

[tex]B=-0.75A+23,000\\-0.75A+23,000 = A+2,000\\A= 12,000\\B=14,000[/tex]

$12,000 were invested at 3% and $14,000 were invested at 4%.

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