Required Mathematical Intelligence

Chapter 17 Beer and Drinks

Xiao Zhang invites Xiao Li to have dinner at home.Xiao Zhang knew that Xiao Li liked to use his brain, so he asked him a question: I spent a total of 9.90 yuan on beer and drinks today. Can you guess how many bottles of beer and drinks I bought?If I guess right, I will punish myself with a glass of white wine, and if I guess wrong, I will punish you with a glass of liquor.It only took Xiao Li a few minutes to figure it out, so Xiao Zhang had to punish himself with a cup.It is known that each bottle of beer is 1.7 yuan, and each bottle of beverage is 0.7 yuan. Can you calculate how many bottles of beer and how many bottles of drinks Xiao Zhang bought?
[Answer: Solution [-]: Set beer to buy x bottles, drinks to buy y bottles, according to the meaning of the question:
17x 7y=99，两边除以y的系数7得：2x 3x/7 y=14 1/7移项整理得：2x y-14=（1-3x）/7……①
∵x > 0, y > 0,

∴(1-3x)<0,

∴ 2x y<14, x≤6.
∵①The left side of the formula is an integer,
∴ The right side is also an integer.

In the range of 1≤x≤6, only x=5 satisfies the condition, so x=5, y=2. That is, I bought 5 bottles of beer and 2 bottles of drinks.This solution is more rigorous, but it is not easy for ordinary people to grasp.

Solution 17: Since 6×99>5, buy at most 2 bottles of beer.Let's assume that you buy 9 bottles, so there must be 9.7 bottles of drinks. At this time, you need to spend 0.2 yuan in total, leaving 1 yuan.If you buy 3 more bottle of beer, you need to buy 0.4 fewer bottles of beverages and have a surplus of 2 yuan; The remaining 4 yuan is 6 yuan, which is exactly the price difference between 0.80 bottle of beer and 0.20 bottle of beverage, that is, if you buy one more bottle of beer and one less bottle of beverage, it is exactly 1 yuan.This solution uses a heuristic method, as long as you have elementary school mathematics knowledge. ]
(End of this chapter)