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Oxana [17]
3 years ago
11

You invest a total of $5800 in two investments earning 3.5% and 5.5% simple interest. Your goal is to have a total annual intere

st income of $283. Write a system of linear equations that represents this situation where x represents the amount invested in the 3.5% fund and y represents the amount invested in the 5.5% fund. Solve this system to determine the smallest amount that you can invest at 5.5% in order to meet your objective.
Mathematics
1 answer:
attashe74 [19]3 years ago
4 0
The annual interest that can be earned through investment of an amount at a simple interest can be calculated through the equation,
                I  = P x (i)
where I is interest, P is the principal amount, and i is the decimal equivalent of the interest. 

Let x be the amount deposited with 3.5% interest. With this representation, the amount deposited with 5.5% is 5800 - x. 

The linear equation that would represent the given scenario is,
        x(0.035) + (5800 - x)(0.055) = 283

Simplifying the equation,
 
       0.035x + 319 - 0.055x = 283

Combining like terms,
           -0.02x = -36
Dividing by -0.02,   
               x = 1800
             $5800 - x = $5800 - $1800 = y
                   y = $4000

Hence, the value that should be deposited to the 5.5% is $40000.   
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