Problema Solution

A woman invests $31,000, part at 8% and the rest at 9 1/2% annual interest. If the 9 1/2% investment provides $582.50 more income than the 8% investment, how much is invested at each rate?

Answer provided by our tutors

X = amount invested at 8%

Y = amount invested at 9 1/2% = 9.5%

X + Y = 31000

Income from 8% investment = 0.08*X

Income from 9% investment = 0.095*Y

0.095*Y = 0.08*X + 582.50

We have the following system of equations for X and Y:

X + Y = 31000

0.095*Y = 0.08*X + 582.50

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click here to see the system of equations solved for X and Y

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X = $1,350

Y = $1,750

$1,350 is invested at 8% and $1,750 at 9 1/2% annual rate.