F.2 Maths

Pegasus

For a three-digit number , the sum of the hundreds digit is 12 . When these two digits are interchanged , the value of the number decreases by 594 . If the tens digit is 5 , find orginal number .
show your steps carefully
thanks

Harpuia

有冇中文........

細薯

>>the sum of the hundreds digit is 12<<
即係百位數+十位數+個位數=12??

如果百位數+個位數=12
我就識計.......
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For a three-digit number , the sum of the hundreds digit is 12 . When these two digits are interchanged , the value of the number decreases by 594 . If the tens digit is 5 , find orginal number .
show your steps carefully
thanks
===============================================
(ng記得英文個term tim......)
let x  and y be the 百位數 and the 個位數 respectively.

x + y  = 12         -------------------(1)

the original number is :


When these two digits are interchanged,the new number is :
100y + 50 + x

Therefore, we have
(100x + 50 + y) - (100y + 50 + x) = 594    ---------------------(2)
99x - 99y = 594
x - y = 6
x = y +6      --------------------(3)

sub. x = y +6 into (1),
2y + 6 = 12
y = 3

Therefore,
x = 9

oscar

Originally posted by Pegasus at 2005-3-15 21:32:
For a three-digit number , the sum of the hundreds digit is 12 . When these two digits are interchanged , the value of the number decreases by 594 . If the tens digit is 5 , find orginal number .
...

很簡單哩...

Let x and y be the hundreds and units digits respectively.
x+y=12 --- (1)
(100x+50+y)-(100y+50+x)=594 --- (2)
Rearrange (2),
100x+50+y-100y-50-x-594=0
99x-99y-594=0 --- (2)'
From (1), y=12-x --- (3)
Substitue (3) into (2)',
99x-99(12-x)-594=0
99x-1188+99x-594=0
198x=1782
x=9
Substitue x=9 into (3),
y=12-9=3
Therefore, The original number is 953.

[ Last edited by oscar on 2005-3-16 at 05:57 PM ]

細薯

The original number is953
寫錯左丫~~

oscar

Originally posted by smallpotato226 at 2005-3-16 17:55:
The original number is953
寫錯左丫~~

係喎....我錯左tim....

細薯

Originally posted by oscar at 2005-3-16 05:56 PM:

係喎....我錯左tim....

寫左new 果個...XD
不要緊~

Pegasus

唔該哂,原來係計錯數