SOLUTION: How can $54,000 be invested, part at 8% annual simple interest and the remainder at 10% annual simple interest, so that the interest earned by the two accounts will be equal ?

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Question 373548: How can $54,000 be invested, part at 8% annual simple interest and the remainder at 10% annual simple interest, so that the interest earned by the two accounts will be equal ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = the interest earned by both accounts
Let b = portion of $54000 invested at 8%
Let c = portion of $54000 invested at 10%
given:
b+%2B+c+=+54000
.08b+=+.1c
8b+=+10c
-----------------
b+=+%285%2F4%29%2Ac
by substitution:
%285%2F4%29%2Ac+%2B+c+=+54000
%289%2F4%29%2Ac+=+54000
c+=+%284%2F9%29%2A54000
c+=+24000
and
b+%2B+c+=+54000
b+=+54000+-+24000
b+=+30000
$30,000 was invested at 8%
and $24,000 was invested at 10%