SOLUTION: Joe has $40,000 to invest. He invests part of it at 5%, one-fourth of this amount at 6%, and the rest of the money at 7%. His total annual interest income is $2,530. Find the am

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Joe has $40,000 to invest. He invests part of it at 5%, one-fourth of this amount at 6%, and the rest of the money at 7%. His total annual interest income is $2,530. Find the am      Log On

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Question 30970: Joe has $40,000 to invest. He invests part of it at 5%, one-fourth of this amount at 6%, and the rest of the money at 7%. His total annual interest income is $2,530. Find the amount invested at each rate.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
.05+%2A+x+%2B+.25+%2A+.06+%2A+x+%2B+.07+%2A+%284%2A10%5E4+-+%285%2F4%29%2Ax%29+=+2530
note that (5/4)*x is (1 + 1/4)*x or x + (1/4)*x which is the amounts
that are NOT invested at 7%, so 40000 - (5/4)*x is the amount invested
at 7%
.05+%2A+x+%2B+.25+%2A+.06+%2A+x+%2B+.07+%2A+4%2A10%5E4+-+.07+%2A+%285%2F4%29%2Ax+=+2530
.05+%2A+x+%2B+.015+%2A+x+%2B+.07+%2A+4%2A10%5E4+-+.0875+%2A+x+=+2530
.065+%2A+x+%2B+.07+%2A+4%2A10%5E4+-+.0875+%2A+x+=+2530
.065+%2A+x+%2B+2800+-+.0875+%2A+x+=+2530
-.0225+%2A+x+%2B+2800++=+2530
-.0225+%2A+x++=+2530+-+2800+
-.0225+%2A+x++=+-270
+x+=+12000
%281%2F4%29+%2A+x+=+3000
4+%2A+10%5E4+-+%28%285%2F4%29+%2A+x%29+=+25000
check

600+%2B+180+%2B+.07+%2A+%2825000%29+=+2530
780+%2B+1750+=+2530
2530+=+2530
OK