SOLUTION: Mardi recieved an inheritance of $70,000. She invested part at 12% and the rest at 9%. Her total annual income from the investments was $8100. Find the amount she invested at 12%

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Question 241447: Mardi recieved an inheritance of $70,000. She invested part at 12% and the rest at 9%. Her total annual income from the investments was $8100. Find the amount she invested at 12%.
Answer by texttutoring(324) About Me  (Show Source):
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You have two unknowns (the amounts invested at each rate), so you need two equations.
Step 1: State your unknowns:
x = amount of $ invested at 12%
y = amount of $ invested at 9%
Step 2: Set up your equations:
Eqn. 1: x+y=70000
Eqn. 2: 0.09*x + 0.12*y = 8100
Step 3: Isolate for y in Eqn. 1:
y = 70000-x
Step 4: Plug this value for y into Eqn. 2, and then collect terms to isolate for x:
0.09*x + 0.12*y = 8100
0.09*x +0.12(70000-x) = 8100
0.09*x +0.12*70000 – 0.12*x = 8100
8400 – 0.03x = 8100
8400 - 8100 – 0.03x = 8100 - 8100
8400 - 8100 – 0.03x = 0
300 = 0.03x
x = 10000
Step 5: Now substitute this back into Eqn. 1 to find y:
y = 70000 – x
y = 70000 – 10000
y = 60000
So the two amounts invested are $10000 at 9% and $60000 at 12%.