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Breakfast 1 yuan, Chinese food 2 yuan, 69 meals a month
(1) There are 4 possibilities.1, breakfast + 2 yuan 1 (Chinese food) + 2 yuan a (dinner)

Price: 1 + 2 + 2 = 5 yuan

2, breakfast + 2 yuan 1 (Chinese food) + 3 yuan a (dinner)

Price: 1 + 2 + 3 = 6 yuan

3, breakfast + 3 yuan 2 (Chinese food) + 2 yuan a (dinner)

The price is: 1 + 3 + 2 = 6 yuan

4, breakfast + 3 yuan 2 (Chinese food) + 3 yuan a (dinner)

The price is: 1 + 3 + 3 = 7 yuan

(2) to take the 1, 2 two kinds of prices, set the first meal price for x days, the second meal price for y days,

that is, x + y = 108, 5x + 6y =600

We get x=48,y=60

So, the first meal price is for 48 days and the second meal price is for 60 days...

The first meal price is for 48 days and the second meal price is for 60 days.