A part of $5000 was invested at 4.5% and a part at 5.5%. The 4.5% investment yields $75 more each year than the 5.5% investment. How much is invested at each rate?

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embizze | High School Teacher | (Level 1) Educator Emeritus

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A $5000 investment was split -- part was invested at 4.5% and the rest at 5.5%. The 4.5% investment yields $75 more in interest than the 5.5% investment.

Let x represent the amount invested at 4.5%:

.045x=.055(5000-x)+75   

** The investment at 4.5% yields .045x (where x is the amount invested at 4.5%). This is equal to the interest earned by the investment at 5.5% plus an additional $75. **

.045x=275-.055x+75
.1x=350                  (Add .055x to both sides and combine like terms.)
x=3500                   (Divide both sides by .1 -- or multiply both sides by 10)

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The amount invested at 4.5% is $3500, while the amount invested at 5.5% is $1500 (5000-3500).

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Check: The interest earned on $3500 invested at 4.5% simple interest in 1 year is 3500(.045)=$157.50

The interest earned on $1500 invested at 5.5% simple interest for 1 year is 1500(.055)=$82.50

And $82.50+$75=$157.50 as required.

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