中一數學題

Observe that (X+2) is divisible by 11 and 9,
so (X+2) is divisible by 99.
Also, (X+1) is divisible by 5.
By checking the first few possibilities of X, i.e. (99-2), (198-2), (297-2), (396-2), only (396-2) i.e. 394 is divisibe by 5 after adding 1 to it.
Answer: 394

Hidden assumptions:
1. X>0
2. a,b,c are integers.

X=5a+4
X=9b+7
X=11c+9

1.X=5a+4
2.X=9b+7
3.X=11c+9

What is a,b,c?
X-4=5a
X-7=9b
X-9=11c

5a-9b=3
11c-9b=-2
11c+5a=1
.'. -2+9b+5a=1

5a+9b=3
5a-9b=3
10a=6
a=3/5

.'. x=7

x<500

x=5a+4

x=9b+7

x=11c+9

X&lt;500

X=5a+4
X=9b+7
X=11c+9