SOLUTION: Amy invests a part of $8000 in bonds paying 12% interest. The remainder is in a savings account at 8%. If she receives $840 in interest for 1 year, how much does she have invested

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Question 176578: Amy invests a part of $8000 in bonds paying 12% interest. The remainder is in a savings account at 8%. If she receives $840 in interest for 1 year, how much does she have invested at each rate? (Show the two equations you used and then your solution)
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

Let x=amount invested at 12%
And let y=amount invested at 8%
Now we are told the following:
x+y=$8000---------------------------------eq1
0.12x+0.08y=$840-----------------------------eq2
From eq1, y=$8000-x. Substitute this into eq2 and we have:
0.12x+0.08($8000-x)=$840 get rid of parens
0.12x+$640-0.08x=$840 subtract $640 from each side
0.12x+$640-$640-0.08x=$840-$640 collect like terms
0.04x=$200 divide each side by 0.04
x=$5000----------------------------------amount invested at 12%
substitute x=$5000 into eq1:
$5000+y=$8000 subtract $5000 from each side
y=$3000-------------------------------------amount invested at 8%
CK
0.12*$5000+0.08*$3000=$840
$600+$240=$840
$840=$840
Another way------------------------only 1 equation
Let x=amount invested at 12%
Then $8000-x=amount invested at 8%
0.12x+0.08($8000-x)=$840------------------same equation as before
Does this help???----------ptaylor