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.
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.
