SOLUTION: John invested $8000 for one year, part at 8% interest and the rest at 10%. If John earned $700 in interest, how much is in each account?

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Question 529205: John invested $8000 for one year, part at 8% interest and the rest at 10%. If John earned $700 in interest, how much is in each account?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = amount invested @ 8%
Let +b+ = amount invested @ 10%
given:
(1) +a+%2B+b+=+8000+
(2) +.08a+%2B+.1b+=+700+
-----------------
(2) +8a+%2B+10b+=+70000+
(2) +4a+%2B+5b+=+35000+
Multiply both sides of (1) by 4
and subtract (1) from (2)
(2) +4a+%2B+5b+=+35000+
(1) +-4a+-+4b+=+-32000+
+b+=+3000+
and, since
(1) +a+%2B+b+=+8000+
(1) +a+=+8000+-+3000+
(1) +a+=+5000+
$5,000 is the amount invested @ 8%
$3,000 is the amount invested @ 10%
check answer:
(2) +.08a+%2B+.1b+=+700+
(2) +.08%2A5000+%2B+.1%2A3000+=+700+
(2) +400+%2B+300+=+700+
(2) +700+=+700+
OK