Question

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?

Answer 1

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

`x+y =39000\\-0.08x+0.095y=467.50`

Multiply second equation by 100 and I equation by 8

`8x+8y = 312000\\-8x+9.5y=46750\\----------------------\\17.5y =358750\\y=20500`

`x = 39000-20500 = 18500`

18500 at 8% and 20500 at 9.5%