Quantity relation: how many bottles of water are changed from the empty bottle
The quantity relationship of line test has always been a problem that puzzles us. The overall planning problem is more diverse, flexible, many test points, and it is difficult to really learn well, but there are also some fixed models. Today, Public education through some examples to understand the empty bottle water problem in the overall planning problem.Example 13 mineral water bottles can be exchanged for a bottle of mineral water, there are 9 empty mineral water bottles, ask how many bottles of water can be drunk without buying?A.3 B.4 C.5 D.First step: 9 empty bottles for 3 bottles of water, the first to drink 3 bottles of water;Step 2: after drinking 3 bottles of water, there are 3 empty bottles that can be exchanged for 1 bottle of water.Step 3: Replace 1 bottle of water and then drink 1 empty bottle, 1 empty bottle can not be replaced.So I drank four bottles of water.Example 23 mineral water bottles can be exchanged for a bottle of mineral water, there are 10 empty mineral water bottles, ask how many bottles of water can be drunk without buying?A.3 B.4 C.Example 2 is the same as example 1, but change the number of empty bottles, we might as well deduce it again.The first step: 10 empty bottles for 3 bottles of water, first drink 3 bottles of water;Step 2: after 3 bottles of water are drunk, there are 3 empty bottles and 1 empty bottle which is not used at the beginning. At this time, there are 4 empty bottles which can be exchanged for 1 bottle of water.Step 3: buy 1 bottle of water to drink will leave an empty bottle, and before no one empty bottles, a total of two empty bottles, at the moment we have only two hands empty bottles in principle can not be replaced, but we can borrow a bottle of water to the boss, put the water to drink, you now have three empty bottles to go in a bottle of water can back to the boss.So I drank 5 bottles of water.Through the first two problems, we found that we could deduce the problem of using empty bottles to change water step by step, but it was a waste of time. Moreover, in case of example 2, we also needed to consider the problem of borrowing water, which was quite troublesome.And it’s not hard to see from questions like this that we end up focusing on how many bottles of water we drink, not how many bottles of water we change.We can put the bottle of water = 1 + 1 a empty bottle, according to the question, three empty bottles in 1 bottle of water, can be seen as three empty bottle = 1 bottle water = 1 + 1 empty bottles, through reduction, got the two empty bottle = 1 part water, we are now to take advantage of this law the problem solving: a, 9 empty bottles, water, rounded down is 4 bottles of water;Example two, 10 empty bottles, one portion of water, so I drank 5 bottles of water, which makes it a lot easier to calculate.Therefore, we can summarize A rule about the type of water exchanged for empty bottles: If A empty bottle can be exchanged for one bottle of water, there are A total of B empty bottles, and they can drink A bottle of water at most.Through the above two examples, I believe that we have A certain understanding and understanding of the empty bottle for water. For the empty bottle for water, we should focus on the law of water change: if A empty bottle can be replaced with 1 bottle of water, there are A total of B empty bottles, you can drink A bottle of water at most.So if they tell us the number of empty bottles, we can just apply the rule;If you know how much water you drink after you change the water, you can solve the problem by writing an equation based on this rule.Then we quickly go through some examples to consolidate it!