SOLUTION: On two investments totaling $7,000, Lydia lost 4% on one and earned 6% on the other. If her net annual receipts were $308, how much was each investment?

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Question 1153667: On two investments totaling $7,000, Lydia lost 4% on one and earned 6% on the other. If her net annual receipts were $308, how much was each investment?

Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +A+ = amount invested at 4%
+7000+-+A+ = amount invested at 6%
Use +I+=+P%2Ar%2At+
----------------------------------------------
(1) +I%5B1%5D+=+-A%2A.04%2A1+
(2) +I%5B2%5D+=+%28+7000+-+A+%29%2A.06%2A1+
(3) +I%5B1%5D+%2B+I%5B2%5D+=+308+
-------------------------------------
Add (1) and (2)
+I%5B1%5D+%2B+I%5B2%5D+=+-.04A+%2B+420+-+.06A+
+308+=+420+-+.1A+
+.1A+=+420+-+308+
+.1A+=+112+
+A+=+1120+
and
+7000+-+A+=+5880+
-------------------------------
$1,120 = amount invested at 4%
$5,880 = amount invested at 6%
-------------------------------------
check:
(1) +I%5B1%5D+=+-A%2A.04%2A1+
(2) +I%5B2%5D+=+%28+7000+-+A+%29%2A.06%2A1+
---------------------------------------
(1) +I%5B1%5D+=+-1120%2A.04%2A1+
(1) +I%5B1%5D+=+-44.8+
and
(2) +I%5B2%5D+=+%28+7000+-+A+%29%2A.06%2A1+
(2) +I%5B2%5D+=+5880%2A.06%2A1+
(2) +I%5B2%5D+=+352.8+
and
(3) +I%5B1%5D+%2B+I%5B2%5D+=+308+
(3) +-44.8+%2B+352.8+=+308+
(3) +308+=+308+
OK



Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

On two investments totaling $7,000, Lydia lost 4% on one and earned 6% on the other. If her net annual receipts were $308, how much was each investment?
Let amount invested in fund that lost 4% be F
Then amount invested in fund that gained 6% = 7,000 - F
We then get: - .04F + .06(7,000 - F) = 308
- .04F + 420 - .06F = 308
- .1F = - 112
F, or amount invested in fund that LOST 4%:
Amount invested in fund that GAINED 6%: