s1 數學

Let x be no. of students did not buy the toy dog
20-x be no. of students bought the toy dog


12.5x+(12.5+4)(20-x)=278

12.5x+330-16.5x=278

16.5x-12.5x=330-278

4x=52

x=13

Let x be the total number of students,
y be the number of students who purchase the toy dog, then we have

12.5x + 4.2y = 278
125x + 42y = 2780
42y = 2780 - 125x
y = 2780/42 - 125x/42
= 66 + 8/42 - 125x/42
= 66 - (125x - 8)/42
Since x, y are positive integers, and the unit digit of 125x - 8 can only be 7 or 2,
we check whether the multiples of 42 with unit digit 2 can be of the form 125x - 8.
We have 42*1 = 42, 42*6 = 252, 42*11 = 462, 42*16 = 572, 42*21 = 782,
42*26 = 992, both of which cannot be expressed as 125x - 8 when x is a positive integer, and x cannot be larger than 26, because 12.5*31 is larger than 278.

Hence, there is no solutions for this question.

2006-11-02 23:37:31 補充：
Oops, misread the question...

let x be the no. of students who did not buy toy dog
then 20-x is students who bought toy dog

(12.5+4)(20-x)+12.5x=278
330-4x=278
-4x=-52
x=13

so no. of students os 13