SOLUTION: I'm having a bit of trouble with this problem. Please help me solve this equation: Mischa invests $20,000 into two accounts paying 7% and 9% annual simple interest respectively.

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Question 971339: I'm having a bit of trouble with this problem. Please help me solve this equation:
Mischa invests $20,000 into two accounts paying 7% and 9% annual simple interest respectively. If the total interest earned for the year is $1,550, how much was invested at each rate?
Thank You.
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

Mischa invests $20000 into two accounts paying 7% and 9% annual simple interest respectively.
in account paying 7%=0.07 Mischa invests $x
and in account paying 9%=0.09 Mischa invests $y

if Mischa invests $20000 and earned 1550 in interest, we have
x%2By=20000............eq.1
0.07x%2B0.09y=1550......eq.2=> both side multiply by 100
---------------------------------------
x%2By=20000............eq.1=> both side multiply by 7
7x%2B9y=155000......eq.2
---------------------------
7x%2B7y=140000............eq.1=> both side multiply by 7
7x%2B9y=155000......eq.2
------------------------------subtract eq.1 from eq.2
7x-7x%2B9y-7y=155000-140000
2y=15000
y=15000%2F2
highlight%28y=7500%29
now, find x
x%2B7500=20000............eq.1
x=20000-7500
highlight%28x=12500%29
so, Mischa invests highlight%28x=12500%29 in account paying 7% , and highlight%28y=7500%29 in account paying 9%
check if 7% of 12500 and 9% of 7500 equal to earning 1550 in interest
7% of 12500 is 12500%2A0.07=875
9% of 7500 is 7500%2A0.09=675
then 875%2B675=1550 which confirms our solution