SOLUTION: Lina Chen invested $24,000, part at 8% and the rest at 7.2%. How much did she invest at each rate if her income from the 8% investment is two thirds that of the 7.2% investment

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Question 669866: Lina Chen invested $24,000, part at 8% and the rest at 7.2%. How much did she invest at each rate if her income from the 8% investment is two thirds that of the 7.2% investment
I've started off with
Price * Rate = Interest
8% x 2/3(24000-x) x * (2/3(24000-x))
7.2% 24000-x

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+a+ = amount invested @ 8%
+b+ = amount invested @ 7.2%
given:
(1) +a+%2B+b+=+24000+
(2) +.08a+=+%282%2F3%29%2A.072b+
------------------------
(1) +b+=+24000+-+a+
Multiply both sides of (2) by +1000+
(2) +80a+=+%282%2F3%29%2A72b+
(2) +240a+=+144b+
By substitution:
(2) +240a+=+144%2A%28+24000+-+a+%29+
(2) +240a+=+3456000+-+144a+
(2) +384a+=+3456000+
(2) +a+=+9000+
and, since
(1) +b+=+24000+-+a+
(1) +b+=+24000+-+9000+
(1) +b+=+15000+
$9,000 was invested @ 8%
$15,000 was invested @ 7.2%
check:
(2) +.08a+=+%282%2F3%29%2A.072b+
(2) +.08%2A9000+=+%282%2F3%29%2A.072%2A15000+
(2) +720+=+%282%2F3%29%2A1080+
(2) +2160+=+2%2A1080+
(2) +2160+=+2160+
OK