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 181359This question is from textbook Algebra and Trigonometry Structure and Method
: 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? This question is from textbook Algebra and Trigonometry Structure and Method

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call the amounts invested at 8% and 7.2% x and y respectively
:
x+y=24000..............eq 1
.08x+.072y=(2/3)y......eq 2
:
rewrite eq 1 to x=24000-y and plug that into eq 2
:
.08(24000-y)+.072y=(2/3)y
:
1920-.08y+.072y=(2/3)y
:
1920-.008=(2/3)y
:
5760-.024y=2y........multiplied terms by 3 to eliminate fraction
:
5760=2.024y
:
$highlight%282845.85%29invested at 7.2 %
:
$highlight%2824000-2845.85=21154.15%29invested at 8%