SOLUTION: Remember Little Johnny? He now has two investments that produce a $150 income each month. If $1,000 more is invested at 9% than at 10% per year, how much was invested at each per

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Remember Little Johnny? He now has two investments that produce a $150 income each month. If $1,000 more is invested at 9% than at 10% per year, how much was invested at each per      Log On

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Question 374126: Remember Little Johnny? He now has two investments that produce a $150 income each month. If $1,000 more is invested at 9% than at 10% per year, how much was invested at each percent? There were 12 months in that year.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = amount invested at 9%
Let b = mount invested at 10%
given:
150%2A12+=+1800 interest received during
the year from both investments
(1) a+=+b+%2B+1000
(2) .09a+%2B+.1b+=+1800
------------------
Multiply both sides of (2) by 100
(2) .09a+%2B+.1b+=+1800
(2) 9a+%2B+10b+=+180000
By substitution:
(2) 9%2A%28b+%2B+1000%29+%2B+10b+=+180000
9b+%2B+9000+%2B+10b+=+180000
19b+=+180000+-+9000
19b+=+171000
b+=+9000
And, from (1)
a+=+9000+%2B+1000
a+=+10000
$10,000 was invested at 9% and
$9,000 was invested at 10%