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Anonymous users2024-02-0512 pcs. Let the quantity of goods purchased by A be m, then the total number of goods purchased by the two is 2m, then 8*2m (when all are 8 yuan goods) < 172<9*2m (when all are 9 yuan goods), and the solution is m = 10
At this time, there are two ways to solve the problem, one is to set a total of x pieces of commodities with a unit price of 9 yuan, according to the problem to list the equation, 9x+8*(20-x)=172, and solve x=12
The second is through the comparison method, when all are 8 yuan goods, a total of 160 yuan (8 * 2m) will be spent, and the actual cost is 172 yuan, and the extra 12 yuan is the number of 9 yuan goods.
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Anonymous users2024-02-04Solution: Suppose the two people purchase the same number of goods, both are k;
A buys $8 for x pieces of goods, and buys $9 for $ y items;
B buys 8 yuan for a product, and buys 9 yuan for a product, B for a b;
According to the meaning of the title, x+y=a+b=k
8x+9y)+(8a+9b)=172
From these two equations, we can see that 172=8(x+y)+8(a+b)+(y+b)=8k+8k+(y+b)=16k+(y+b).
i.e. y+b=172-16k. The following is only required to produce k: (using extreme assumptions).
Just imagine: if you use all 172 yuan to buy goods with a unit price of 8 yuan, you can only buy 172 8 pieces at most;
If all 172 yuan is used to buy goods with a unit price of 9 yuan, you can only buy 172 9 pieces at most;
And now there are both 172 yuan goods with a unit price of 8 yuan and a unit price of 9 yuan, so it should be between.
Between 172 9 and 172 8, i.e. 172 9<2k<172 8, it is noted that 2k is an even number, while between 172 9 and .
There is only one "20" for even numbers between 172 and 8, so there is 2k=20, which is k=10
Thus y+b=172-16k=172-160=12, so there are 12 products with a unit price of 9 yuan.
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Anonymous users2024-02-03If there are x pieces of goods with a unit price of 8 yuan, and there are y pieces of skillfully judged goods with a unit price of 9 yuan, then 8x+9y=172, that is, y=(172-8x) 9=4(43-2x) 9
At the same time, it must be satisfied that x and y are both non-negative integers, and x+y is an even number (from "the two people buy the same number of goods" can be seen as filial piety).
Therefore: 43-2x must be a multiple of 9, and the value of x is only: 8, 17, when x=8, y=12, x+y=20, which is in line with the title.
When x=17, y=4, x+y=20, which is in line with the topic.
Therefore, there are 4 or 12 pieces of goods with a unit price of 9 yuan.
There is no good way to improve math, only to do more problems.
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