First of all, it is easy to get a box of Fuwa worth 120 yuan and a badge of 75 yuan.

If there are x second prizes and y third prizes, the first prize is (12-x-y).

* * * to Fuwa: 12-x-y+x= 12-y (box)

Badge: 12-x-y+y= 12-x (pieces)

List the following inequalities:

1000≤ 120( 12-y)+75( 12-x)≤ 1 100

Simplify:

248/3≤5x+8y≤268/3

Because x and y are integers.

So this inequality can be simplified as:

83≤5x+8y≤89

Because x+y

So only one set of positive integer solutions is

x= 1

y= 10

So the first prize, the second prize and the third prize are 1, 1, 10 respectively.

That is, * * * wants to buy two boxes of Fuwa and 1 1 badges.

therefore

Buy Fuwa with 120*2=240 (RMB)

Buy badge 75* 1 1=825 (RMB)

1065 The total cost is between 1000 and100, no problem.