數學難題，請大大幫幫忙

Question

某班有60人，英文合格有32人，中文科合格有42人，2科都不合格有5人，問有多少人2科合格？？？？？

Answer 1

某班有四種人
只是英文科合格, 中文科不合格的人(設做a)
只是中文科合格, 英文科不合格的人(設做b)
兩科都合格的人(設做c)
兩科都不合格的人(設做d)
1)a+c=32
2)b+c=42
3)a+b+C+D=60
D=5
即a+b+C=55
將1)+2)
a+B+2c=74
4)a+B=74-2c
將第四式代入第三條式
(74-2c)+c=55
74-c=55
c=74-55
c=19
2科都合格是19
將c代入去其他數式可以知埋, 只有英文合格和中文合格的人呢

Answer 2

From the question, we know that 55 people pass at least one of chinese or English

So to find the total number of people who pass two subjects, we have
(32 + 42) - 55
= 19

The number (32 + 42) counts the number of people who pass either English or Chinese, however, it may happen that counts may repeat in case some people who pass both subjects, so we subtract the total number of people involved in passing subjects (i.e. 55), we could find the number of people who are double-counted, which represents the people who pass two subjects

Answer 3

2科合格=42+32+5-60=19人