Multiple choice

Tom, a homeowner in Chicago, decided to take a loan of \$40,000 to renovate his house. He borrowed part of the money at an interest rate of 10% per annum, and the rest at an interest rate of 15% per annum. After 1 year, Tom repaid a total of \$5,700 in interest. How much did he borrow at each interest rate?

  1. $6,000 at 10%, $34,000 at 15%
  2. $10,000 at 10%, $30,000 at 15%
  3. $12,000 at 10%, $28,000 at 15%
  4. $15,000 at 10%, $25,000 at 15%
  5. $20,000 at 10%, $20,000 at 15%
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A Correct answer
Explanation

Let x be the amount at 10% and y be the amount at 15%. x + y = 40000 and 0.10x + 0.15y = 5700. Multiplying the first by 0.10 gives 0.10x + 0.10y = 4000. Subtracting this from the second gives 0.05y = 1700, so y = 34000. Then x = 6000.

AI explanation

Let the amount borrowed at 10% be x, so the amount borrowed at 15% is 40000 minus x. The total interest equation for one year is 10% of x plus 15% of (40000 minus x) equals 5700, which simplifies to 0.10x + 6000 - 0.15x = 5700. Solving this gives -0.05x = -300, so x is \$6,000. The amount borrowed at 15% is 40000 minus 6000, which equals \$34,000, meaning Tom borrowed \$6,000 at 10% and \$34,000 at 15%.

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