x = 老板买的一袋白糖
47100g < x < 51500g
x ≡ 400 (mod 600)
x ≡ 100 (mod 500)
it is easy to see that the first simple solution for x is 1600
1600 ≡ 400 (mod 600), can be written as 1600 * (3k + 1) ≡ 400 (mod 600)
1600 ≡ 100 (mod 500), can be written as 1600 * (5q + 1) ≡ 100 (mod 500)
In order to generate an equation that satisfy both statement
the equation come like 1600(15y + 1) ≡ 400 (mod 600), ≡ 100 (mod 500)
⌊51500/1600⌋ = 32
⌊47100/1600⌋= 29
the number that only satisfy y is 2
Hence the answer is 1600 * 31 = 49600g = 49.6kg
P.S: you can also plug in with this formula, with any integer y.
Chinese Version:
x = 老板买的一袋白糖
47100克 < x < 51500克
x ≡ 400 (mod 600)
x ≡100 (mod 500)
很容易看出 x 的第一个简单解是 1600
1600 ≡ 400 (mod 600)，可以写成 1600 * (3k + 1) ≡ 400 (mod 600)
1600 ≡ 100 (mod 500)，可以写成 1600 * (5q + 1) ≡ 100 (mod 500)
为了生成满足这两个陈述的方程
等式为 1600(15y + 1) ≡ 400 (mod 600), ≡ 100 (mod 500)
⌊51500/1600⌋ = 32
⌊47100/1600⌋= 29
只满足y的数为2
因此答案是 1600 * 31 = 49600g = 49.6kg
P.S：您也可以使用此公式代入任意整数 y。
