SOLUTION: Sue invested 10,000, part at 3.8% annual intrest and the balance at 7% annual intrest. How much is invested at each rate if a 1 year intrest payment is 603.68

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Question 556303: Sue invested 10,000, part at 3.8% annual intrest and the balance at 7% annual intrest. How much is invested at each rate if a 1 year intrest payment is 603.68
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = amount invested @ 3.8%
Let +b+ = amount invested @7%
given:
(1) +a+%2B+b+=+10000+
(2) +.038a+%2B+.07b+=+603.68+
multiply both sides of (2) by +1000+
(2) +38a+%2B+70b+=+603680+
Multiply both sides of (1) by +38+
and subtract (1) from (2)
(2) +38a+%2B+70b+=+603680+
(1) +-38a+-+38b+=+-380000+
+32b+=+223680+
+b+=+6990+
and, since
(1) +a+%2B+b+=+10000+
(1) +a+%2B+6990+=+10000+
(1) +a+=+10000+-+6990+
(1) +a+=+3010+
$3,010 = amount invested @ 3.8%
$6,990 = amount invested @7%
check answers:
(2) +.038%2A3010+%2B+.07%2A6990+=+603.68+
(2) +114.38+%2B+489.3+=+603.68+
(2) +603.68+=+603.68+
OK