SOLUTION: A boy invested $860 of his Bar Mitzvah money. He put part of it in the bank at 4.5% interest and lent the remainder to his parents at 7%. If after one year the interest on these in

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: A boy invested $860 of his Bar Mitzvah money. He put part of it in the bank at 4.5% interest and lent the remainder to his parents at 7%. If after one year the interest on these in      Log On


   



Question 1029772: A boy invested $860 of his Bar Mitzvah money. He put part of it in the bank at 4.5% interest and lent the remainder to his parents at 7%. If after one year the interest on these investments was $51.95. Find how much he put in the bank.
PLEASE USE SYSTEMS OF EQUATIONS AND SHOW YOUR WORK !!!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the amount he put in the bank
Let +b+ = the amount he lent to parents
( I'm assuming simple annual interest )
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(1) +a+%2B+b+=+860+
(2) +.045a+%2B+.07b+=+51.95+
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(2) +45a+%2B+70b+=+51950+
(2) +9a+%2B+14b+=+10390+
Multiply both sides of (1) by +9+
and subtract (1) from (2)
(2) +9a+%2B+14b+=+10390+
(1) +-9a+-+9b+=+-7740+
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+5b+=+2650+
+b+=+530+
and
(1) +a+%2B+530+=+860+
(1) +a+=+330+
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He put $330 in the bank
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check:
(2) +.045a+%2B+.07b+=+51.95+
(2) +.045%2A330+%2B+.07%2A530+=+51.95+
(2) +14.85+%2B+37.1+=+51.95+
(2) +51.95+=+51.95+
OK
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