AMC 8 Daily Practice Round 8

Complete problem set with solutions and individual problem pages

Problem 3 Medium

To mortgage my car, I paid half of its price in the first month, then paid \frac{1}{10} of its original price in the second month. I still owe the car company 10,000 dollars. The price of my car is            .

  • A.

    10,000 dollars

  • B.

    15,000 dollars

  • C.

    20,000 dollars

  • D.

    25,000 dollars

  • E.

    30,000 dollars

Answer:D

The total paid in the first two months is: 50\% + 10\% = 60\%

The remaining unpaid amount is: 40\%.

Since this remaining 40\% corresponds to 10{,}000 dollars, the full price of the car is: \frac{10{,}000}{40\%} = 25{,}000 \text{ dollars}

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