SOLUTION: Peggy invested $1000, part at 8% per annum and the remainder at 9% per annum. After one year, her total interest from these investments was $84. How much did she invest at each r

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Peggy invested $1000, part at 8% per annum and the remainder at 9% per annum. After one year, her total interest from these investments was $84. How much did she invest at each r      Log On


   

Question 516807: Peggy invested $1000, part at 8% per annum and the remainder at 9% per annum. After one year, her total interest from these investments was $84. How much did she invest at each rate?
How would you solve this question? What would the let statements be? Can you please guide me through the process.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the amount Peggy invested at 8% per annum, then the remainder ($1000-x) was invested at 9% per annum. The total interest earned on these two amounts is given as $84.00
We can express the interest earned on the two amounts as:
0.08x as the interest earned on amount x at 8% and 0.09(1000-x) as the amount earned on the remainder at 9%. The sum of these two amounts is given as $84.00 so this can be expressed in the equation:
0.08x+0.09(1000-x) = 84 Simplify and solve for x.
0.08x+90-0.09x = 84
-0.01x+90 = 84 Subtract 90 from both sides.
-0.01x = -6 Divide by -0.01
x = 600 and 1000-x = 400
Peggy invested $600 at 8% per annum and $400 at 9% per annum.