Help!我有條數學題唔識 (F4)

2009-08-07 6:12 am
The value of a two-diit number is 3 times the sum of the two digits. If 9 is added to this two-digit number, the new value will be 4 times the sum of the two digits. Find the two-digit number.

回答 (2)

2009-08-07 6:35 am
✔ 最佳答案
Assuming the first digit is A and the second is B,

10A+B=3(A+B)..............(1)
10A+B+9=4(A+B)..............(2)

From (1),

7A=2B
B=3.5A.......................(3)

From (2),

6A+9=3B...................(4)

Inserting (3) into (4),

6A+9=3(3.5A)
A=2

Inserting A=2 into (3),

B=3.5(2)
B=7
2009-08-07 6:35 am
Please understand that 97= 9*10+7 and a number ab is equal to
a*10+b



Let a be the ten digit number, Let b be the unit digit number

(From the first sentence, we know that:)

3*(a+b) = 10a+b

3a+3b = 10a+b

7a = 2b...................................................(1)

(From the second sentence, we know that:)

4*(a+b) = 10a+b+9

4a+4b = 10a+b+9

3b = 6a+9

b= 2a+3.....................................................(2)

Sub (2) into (1)

7a = 2*(2a+3)

7a = 4a+6

3a = 6

a = 2

Sub a=2 into (2)

b = 2(2)+3

b = 7
參考: My brain


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