一條Math Question*

2007-07-11 6:31 pm

The ten-digit of a three-digit number is twice its hundreds-digit, and its units-digit is greater than its hundreds-digit by 3. If the hundreds-digit is increased by 50%, the tens-digit remains unchanged and the unit-digit is decreased by 40%, the value of the number will be increased by 40%. Find the original number.

答案係幾多??

回答 (2)

Yue Hung

2007-07-11 9:59 pm

✔ 最佳答案

假設原來數字的百位、十位和個位是 a、b和c，所以原來數字的數值是 100a + 10b + c。

從題意，新的數字的數值是 100(1.5a) + 10b + 0.6c = 150a + 10b + 0.6c。因此，我們有

1.4 (100a + 10b + c) = 150a + 10b + 0.6c ... (1)

另外，十位是百位的兩倍，即 b = 2a ... (2)
個位比百位大 3，即 c = a + 3 ... (3)

將(2)及(3)代入(1)，我們有

1.4(100a + 10(2a) + a + 3) = 150a + 10(2a) + 0.6(a + 3)
1.4(121a + 3) = 170.6a + 1.8
1694a + 42 = 1706a + 18
12a = 24
a = 2

所以，原來的數字是 245。

👍 0 👎 0

CKCHUNG

2007-07-15 5:50 am

V. Details

👍 0 👎 0