Required Mathematical Intelligence

Chapter 9 Buying Cigarettes
Harbin in the 20s.One day, an unexpected visitor came to a small shop.He said to the salesman: I am a southerner who is on a business trip to Harbin, and I want to bring back the Harbin specialty "Harbin, Yingchun, Grape" cigarettes for everyone to taste.I only have 60 yuan now, and I can buy all the cigarettes.The prices at that time were 3 yuan, 0.29 yuan and 0.27 yuan respectively.After calculating, the salesman satisfied his request.How many boxes of each cigarette did this southerner buy?
[Answer: It is best to use the method of solving "indeterminate equations" for this question, otherwise you can only use the "testing" method.Suppose you buy a box of grapes and winter jasmine, and buy Harbin cigarettes with all the remaining money. You can buy 10 boxes in total.Let us also buy one box each of Yingchun and Harbin Tobacco, and buy grape cigarettes with the remaining money. A total of 12 boxes can be bought. That is to say, customers can buy at least 10 boxes and at most 12 boxes.First look at the situation of buying 10 boxes, assuming that Harbin, Yingchun, and Putaoyan buy x, y, and z boxes respectively, the indeterminate equation can be listed:

29x 27y 23z=300①

xyz=10②

After solving y=10-xz from ② and substituting it into ①, we get:
2z=x-15③

∵x≤8, z≥1
∴ There is no solution to formula ③

Change the 10 in the ② formula to 11, and finally get: 2x=3 4z, the left side is an even number, the right side is an odd number, and there is no solution.Finally, change 11 to 12, and get: 2z=12 x, set x=2 (only even numbers can be taken), get z=7, y=3, then set x=4, get: z=8, y =0, does not meet the requirements. x cannot be larger, so there is only one answer, namely:
Buy 2 boxes of Harbin brand, 3 boxes of Yingchun brand, and 7 boxes of Grape brand. ]
(End of this chapter)