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?

Question 171870This question is from textbook Algebra and Trigonometry: Structure and Method-Book 2
: 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-Book 2

Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
This has a little twist from the normal problems like this ....the interest earned is a total of the 8% investment and 7.2% investment...lets call the amount earned by 7.2% investment B.....therefore the amount earned by the 8% investment is 2/3B. Lets call the ammount invested at 8% x and the amount invested at 7.2% 24000-x
:
.08x=(2/3)B---->mult by 3-------------------------->.24x-2B=0.....eq 1
.072(24000-x)=B-->distribute----->1728-.072x=B---->.072x+B=1728...eq 2
:
multiply eq 2 by 2 and add it to eq 1........eliminating the B terms
:
.24x+.144=3456
:
.384x=3456
:
amount invested at 8%
:
amount invested at 7.2%

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