SOLUTION: Write a system of two equations in two variables to solve the problem. A woman invested some money at 8% and some at 9% annual simple interest. The interest for 1 year on the co

Question 868799: Write a system of two equations in two variables to solve the problem.
A woman invested some money at 8% and some at 9% annual simple interest. The interest for 1 year on the combined investment of $10,000 was $840. How much was invested at each rate?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Part I 8.00% per annum ------------- Amount invested =x
Part II 9.00% per annum ------------ Amount invested = y
10000
Interest----- 840.00

Part I 8.00% per annum ---x
Part II 9.00% per annum ---y
Total investment
x + 1 y= 10000 -------------1
Interest on both investments
8.00% x + 9.00% y= 840
Multiply by 100
8 x + 9 y= 84000.00 --------2
Multiply (1) by -8
we get
-8 x -8 y= -80000.00
Add this to (2)
0 x 1 y= 4000
divide by 1
y = 4000
Part I 8.00% $ 6000
Part II 9.00% $ 4000

CHECK
6000 --------- 8.00% ------- 480.00
4000 ------------- 9.00% ------- 360.00
Total -------------------- 840.00

m.ananth@hotmail.ca

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