_桃子一个3分钱,梨一个4分钱,樱桃1分钱6个!怎么花1块钱吃100个水果!的答案

2025-03-14 22:12:16
推荐回答(2个)
回答1:

解:设买桃子X个, 梨Y个 ,樱桃Z个;
3X+4Y+Z/6=100 ①
X+Y+Z=100 ②
由①式得:
18x+24y+z=600 ③
③-②得:17x+23y=500
x=(500-23y)/17
因为x,y,z均为正整数
(500-23y)/17≥1
500-23y≥17
23y≤483
y≤21
即:1≤y≤21
当y=4时,x=24,z=72

当y=21时,x=1,z=78

答:花1块钱,买24个桃子,4个梨子和72个樱桃;或者买1个桃子,21个梨子和78个樱桃。

回答2:

列方程不能解题的,必须用逻辑+推测。
以最便宜的樱桃为已知个数,推测桃子与梨子的个数,如果矛盾就舍弃。
假设樱桃吃100个,花费100/6=16.7分钱,再也不能吃桃子和梨子了,不能花完1块钱,可排除。
因必须花1块钱,是整数,所以樱桃吃的个数必须是6的倍数。
吃樱桃(个)花费钱数(分)剩余钱数(分)最多能吃桃/梨(个)能最多或最少再花钱(分)
96 16 84 4 16
90 15 85 10 40 84 14 86 16 64
78 13 87 22 88
72 12 88 28 84(最少)
66 11 89 34 102(最少)
依据题意,吃樱桃96、90、84、66及66以下均可以排除,符合题意的只有吃樱桃78、72个。
假定吃樱桃78个,假设吃桃子X个,梨子为100-78-X个,列方程如下:
3*X+4*(100-78-X)+78/6=100
解方程,X=1(个),成立。
答:吃桃子1个,梨子为21个,樱桃78个,共计100个水果,正好花费了100分钱(1块钱)。

再假定吃樱桃72个,假设吃桃子X个,梨子为100-72-X个,列方程如下:
3*X+4*(100-72-X)+72/6=100
解方程,X=24(个),成立。
答:吃桃子24个,梨子为4个,樱桃72个,共计100个水果,正好花费了100分钱(1块钱)。

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