The questionnaire survey was conducted on 40 sixth graders in an elementary school.
The questionnaire was as for three subjects, language, mathematics (Sansue) and science, if they like it, mark o, if they do not like it, mark ×.
The grand total of o was 100 and that of × was 20.
There was no pupil who marked × to all three subjects.
There are 35 pupils who marked o to mathematics.
Among these, there are two pupils who marked o only to mathematics and four students who marked x to mathematics and o to science.
Answer the following questions.
(1) Find the number of the pupil who marked o only to language.
(2) Find the number of pupil at most who marked o to all three subjects.
The questionnaire was as for three subjects, language, mathematics (Sansue) and science, if they like it, mark o, if they do not like it, mark ×.
The grand total of o was 100 and that of × was 20.
There was no pupil who marked × to all three subjects.
There are 35 pupils who marked o to mathematics.
Among these, there are two pupils who marked o only to mathematics and four students who marked x to mathematics and o to science.
Answer the following questions.
(1) Find the number of the pupil who marked o only to language.
(2) Find the number of pupil at most who marked o to all three subjects.
Answer
Solution
(1) There are 35 pupils who marked o to mathematics and four pupils who marked × to mathematics and marked o to science in total 40 pupils.
This shows that there are 35 + 4 = 39 pupils who marked o to mathematics or science.
There is no person who marked x to all three subjects.
Therefore, the number of the pupil who marked o only to language is 40 - 39 = 1 person.
(2) The table as shown below can be created from problem sentence and the result of (1).
In order to increase the number of the pupil who marked o to all three subjects as many as possible, it is to lessen the number of x as many as possible in 3~35 pupils in a table.
Since there are 20 × in all, if language of the pupil of 36~39 is also set to ×, the number of × will be decreased in the frame of 3~35.
Thus, × will be 14 pieces in all into 1, 2, and 36~40, and the remainder is 20 - 14 = 6 pieces.
Since there are two persons who marked o only to mathematics, × is marked only one piece to any of 33 persons among 3~35.
Six remaining × will be only one piece to one person.
Therefore, there are 33 - 6 = 27 persons at most who marked o to all three subjects.
(1) one
(2) 27
(2) 27
(1) There are 35 pupils who marked o to mathematics and four pupils who marked × to mathematics and marked o to science in total 40 pupils.
This shows that there are 35 + 4 = 39 pupils who marked o to mathematics or science.
There is no person who marked x to all three subjects.
Therefore, the number of the pupil who marked o only to language is 40 - 39 = 1 person.
(2) The table as shown below can be created from problem sentence and the result of (1).
In order to increase the number of the pupil who marked o to all three subjects as many as possible, it is to lessen the number of x as many as possible in 3~35 pupils in a table.
Since there are 20 × in all, if language of the pupil of 36~39 is also set to ×, the number of × will be decreased in the frame of 3~35.
Thus, × will be 14 pieces in all into 1, 2, and 36~40, and the remainder is 20 - 14 = 6 pieces.
Since there are two persons who marked o only to mathematics, × is marked only one piece to any of 33 persons among 3~35.
Six remaining × will be only one piece to one person.
Therefore, there are 33 - 6 = 27 persons at most who marked o to all three subjects.
