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.