SOLUTION: Fran received $113 per year in simple interest from investing $1300.00 Part is invested at 7% and part at 8% and part at 9%. There is 800 more invested at 9% than 8%. Find the amou

Algebra ->  College  -> Linear Algebra -> SOLUTION: Fran received $113 per year in simple interest from investing $1300.00 Part is invested at 7% and part at 8% and part at 9%. There is 800 more invested at 9% than 8%. Find the amou      Log On


   



Question 267227: Fran received $113 per year in simple interest from investing $1300.00 Part is invested at 7% and part at 8% and part at 9%. There is 800 more invested at 9% than 8%. Find the amount invested at 9%.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = amount invested @ 7%
Let b = amount invested @ 8%
Let c = amount invested @ 9%
given:
(1) a+%2B+b+%2B+c+=+1300
(2) .07a+%2B+.08b+%2B+.09c+=+113
(3) c+=+b+%2B+800
---------------------
Multiply both sides of (2) by 100
(2) 7a+%2B+8b+%2B+9c+=+11300
Multiply both sides of (1) by 7
and subtract (1) from (2)
(2) 7a+%2B+8b+%2B+9c+=+11300
(1) -7a+-+7b+-+7c+=+-9100
b+%2B+2c+=+2200
And from (3):
b+=+c+-+800
By substitution:
c+-+800+%2B+2c+=+2200
3c+=+3000
c+=+1000
$1000 was invested @ 9%
check answer:
b+=+c+-+800
b+=+1000+-+800
b+=+200
a+%2B+b+%2B+c+=+1300
a+%2B+200+%2B+1000+=+1300
a+=+1300+-+1200
a+=+100
and
.07%2A100+%2B+.08%2A200+%2B+.09%2A1000+=+113
7+%2B+16+%2B+90+=+113
113+=+113
OK