# 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?

embizze | High School Teacher | (Level 2) 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.