Math  /  Algebra

QuestionMichelle borrows a total of $6000\$ 6000 in student loans from two lenders. One charges 3.6%3.6 \% simple interest and the other charges 5.6%5.6 \% simple interest. She is not required to pay off the principal or interest for 3 yr. However, at the end of 3 yr, she will owe a total of $738\$ 738 for the interest from both loans. How much did she borrow from each lender?
Part: 0/20 / 2
Part 1 of 2
Michelle borrowed \ \squareat at 3.6 \%$.

Studdy Solution
Solve the system of equations to find the amount borrowed from each lender.
From Equation 1, express y y in terms of x x : y=6000x y = 6000 - x
Substitute y=6000x y = 6000 - x into the simplified Equation 2: 0.108x+0.168(6000x)=738 0.108x + 0.168(6000 - x) = 738
Distribute and simplify: 0.108x+10080.168x=738 0.108x + 1008 - 0.168x = 738
Combine like terms: 0.06x+1008=738 -0.06x + 1008 = 738
Subtract 1008 from both sides: 0.06x=7381008 -0.06x = 738 - 1008 0.06x=270 -0.06x = -270
Divide both sides by -0.06: x=2700.06 x = \frac{-270}{-0.06} x=4500 x = 4500
Michelle borrowed \4500at4500 at 3.6\%$.

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