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A new three digit number is obtained by transposing a three digit number and a hundred digit number. It is known that the product of the two three digits is equal to 52605, then the sum of the two three digits is equal to 52605______ ．
52605 = 3 × 3 × 5 × 7 × 167, so 52605 = 105 × 501; 105 + 501 = 606
Transpose a three digit number and a hundred digit number to get a new three digit number. It is known that the product of the two three digit numbers is equal to 52605, then
52605=105*501
The two three digits are 105501
For a three digit number, the sum of each digit is 16, and the ten digit number is the sum of a digit and a hundred. If the hundred and a hundred are transposed, then the new number is 594 larger than the original number, and the original number is calculated
There is a three digit number, and the sum of the digits is 16. The ten digit number is the sum of the one digit number and the hundred digit number. If the hundred digit number is exchanged with each digit, then the new number is 594 larger than the original number, and the original number can be calculated. (use equation)
We use the quadratic equation of two variables
Let the individual bit and the ten bit be x and Y respectively, then the hundred bit is (16-x-y)
y=x+(16-x-y)
100(16-x-y)+10y+x+594=100x+10y+(16-x-y)
It is concluded that y = 8
Substituting: 100 (8-x) + X + 594 = 100x + 8-x
99（8-x）+594=99x
72-9x+54=9x
x=1
Then the number is 781
In this paper, the linear equation of one variable is used
The sum of each digit is 16, and ten digit is the sum of one digit and hundred digit
It is concluded that "the number of tens is 16 / 2 = 8
If the digit is x, then the hundred is (8-x)
100x+8*10+（8-x）=100（8-x）+10*8+x+594
Simplification: 99x = 99 (8-x) + 594
(about 11 on both sides): 9x = 9 (8-x) + 54
18x=18
x=1
Then the number is 781
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