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.
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.
