The portion of the loan 11% is 23000(0.4954) = $11,394.2
And the portion of the loan 15% is 23000(0.3045) = $7015
Let x be the amount loaned at 11% annual interest so that 23000-x represents the amount loaned at 12% annual interest.
The total interest earned for both loans was $2,595.00 so we can write:
23000(P) = $2,595
P = 0.09 or 9.00 %
This number is a weighed average of the 4% yield and the 15% yield so the next equation to solve is
9.00 = 11 (1 – X) + 12X
Where X is the proportion of the loan given at the indicated interest. So
10.55 = 11 – 11X + 12X
5.45 = 11X
X = 0.4954
1-X = 0.3045
So the portion of the loan 11% is 23000(0.4954) = $11,394.2
And the portion of the loan 15% is 23000(0.3045) = $7015
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