Requesting a mathematical diary of traveling (within Shandong Province)

Mathematical Diary 3

Month, Day, Week

In the evening, I saw a difficult problem in the Olympiad book: There are three times as many apple trees in the orchard as there are pear trees. , Master Lao Wang fertilizes 50 apple trees and 20 pear trees every day. After a few days, all the pear trees have been fertilized, but there are still 80 apple trees that have not been fertilized. I would like to ask: How many apple trees and pear trees are there in the orchard?

I was not intimidated by this question, the difficult problem stimulated my interest. I think that apple trees are three times as large as pear trees. If both trees are to be fertilized on the same day, Master Wang should fertilize "20×3" apple trees and 20 pear trees every day. In fact, he only fertilized 50 apple trees every day, a difference of 10 trees, and finally a difference of 80 apple trees. From this, we can know that Master Lao Wang has been fertilizing for 8 days. There are 20 pear trees in one day, which means 160 pear trees in 8 days. Based on the first condition, we can know that there are 480 apple trees. This is to use the idea of ????hypothesis to solve problems, so I think the hypothesis method is actually a good way to solve problems.