With the examination questions of mathematical operation in the civil service examination getting closer to life and paying attention to reality, the probability of coordinating types (empty bottles for water, multi-person cooperation, goods concentration, crossing bridges, etc.) is increased. ) are increasing. The problem of overall planning is often encountered in daily life, and it is to study how to save time and increase efficiency. Therefore, it is necessary for us to focus on the issue of overall planning.
How to review the overall problem and how to solve it? The first impression of this kind of problem is: "How to solve this problem! ! ! "However, when we have mastered the problem-solving skills of each type of question, many problems may be just verbal problems for us. Next, Chinese public education experts will interpret it for you.
Take changing empty bottles for water as an example: the characteristics of changing empty bottles for water are easy to distinguish. There are two main types: First, there are n empty bottles, and then the topic will tell the exchange rules and ask me how many bottles of water I can drink for free. The second is: there are n people, and then inform the exchange rules, asking to ensure that everyone drinks a bottle of water, and asking how many bottles at least need to be purchased?
Example 1: It is known that five empty bottles can be exchanged for one bottle of water. There are 45 empty bottles now. How many bottles of water can I drink for free?
According to the general idea, we must directly calculate 45÷5=8 bottles of water ... 5 empty bottles, 8+5= 13 empty bottles, and we can change, 13÷5=2 bottles of water ... 3 empty bottles, 3+2=5 empty bottles. Of course, this will eventually get the correct answer, but it is obviously slower and more complicated.
If we look at a bottle of water in a different way: 1 bottle water = 1 bottle water+1 empty bottle, the exchange rule is: 5 empty bottles = 1 bottle water +0 empty bottles, so it is equivalent to 4 empty bottles. (Note: this 1 1 bottle of water only includes the water in the bottle, not the empty bottle. )
Example 2: It is known that four empty bottles can be exchanged for one bottle of water. Now 37 students in the class go out to play. How many bottles can I buy as a monitor to ensure that everyone drinks a bottle of water?
China public's analysis of such problems needs to be considered together with life. As we all know, in real life, as a monitor, we can't buy some water first, let these people drink it quickly, put away the empty bottles after drinking, and then change the water to those students who haven't drunk it. If we do this, the monitor will definitely be ousted. Our usual practice is to buy enough bottles for the whole class at a time, one for each person, and when everyone finishes drinking, put away everyone's empty bottles to see how many bottles of water are worth and give less money. Therefore, in order to solve the above problems, the monitor must have bought 37 bottles at a time, and after everyone drank them, 37 empty bottles were produced, 37 ÷ 4 = 9... 1, which means that 37 empty bottles are worth 9 bottles of water, and there will be 1 empty bottles left, so we can pay 9 bottles of water less and/kloc-0 left. Therefore, you need to spend at least 37-9=28 bottles of water.