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Phyllis invested 74000 dollars, a portion earning a simple interest rate of 5 percent per year

Phyllis invested 74000 dollars, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 7 percent per year. After one year the total interest earned on these investments was 4480 dollars. How much money did she invest at each rate?

At rate 5 percent :
At rate 7 percent :

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1 Answer

Begin by defining variables:

x = Amount invested at 5%

y = Amount invested at 7%

Using the information from the problem, we can see that the amount invested at 5% (x) plus (+) the amount invested at 7% (y) equals (=) 74,000.

x + y = 74,000                        Equation 1

The amount invested in at 5% (x) times the rate of return (.05) gives us the amount of return from the money invested at 5%.  The amount invested at 7% (y) times the rate of return (.07) gives us the amount of return from the money invested at 7%.  When these returns are added together, we get the total amount of interest earned on the investments (4480).

.05x + .07y = 4480                  Equation 2

Now that we have a system of 2 equations in 2 variables, we can use substitution or elimination to solve the system.  I am going to use substitution.

x + y = 74,000                              Equation 1

x + y - y = 74,000 - y                     Subtract y from each side

x = 74,000 - y                               Simplify

.05x + .07 y = 4480                       Equation 2

.05(74,000 - y) + .07y = 4480        Substitute the value of x from equation 1 into equation 2

3700 - .05y + .07y = 4480              Distribute the .05

3700 + .02y = 4480                       Simplify

3700 + .02y - 3700 = 4480 - 3700   Subtract 3700 from each side

.02y = 780                                     Simplify

.02y/.02 = 780/.02                          Divide each side by .02

y = 39,000                                      Simplify

x = 74,000 - y                                  Equation 1 solved for x

x = 74,000 - 39,000                         Substitution

x = 35,000                                     Simplify

She invested $35,000 at 5% and $39,000 at 7%.

 

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