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A woman invests $39,000, part at 8% and the rest at 9 1 2 % annual interest. If the 9 1 2 % investment provides $467.50 more income than the 8% investment, how much is invested at each rate?

Respuesta :

Answer:

Step-by-step explanation:

Amount invested 39000 dollars

Let x be invested at 8% and y at 9.5%

Then interest on X = 0.08x and interest of Y =0.095 Y

The equations that connect x and y are

[tex]x+y =39000\\-0.08x+0.095y=467.50[/tex]

Multiply second equation by 100 and I equation by 8

[tex]8x+8y = 312000\\-8x+9.5y=46750\\----------------------\\17.5y =358750\\y=20500[/tex]

[tex]x = 39000-20500 = 18500[/tex]

18500 at 8% and 20500 at 9.5%

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