There was an election of the president of student council in a certain junior high school and three persons, Taro, Jiro, and Hanako, stood as a candidate.
A pie chart expresses the rate of the number of votes obtained by each person.
The ratio of the number of boys students and girls students of this junior high school 5 : 7.
The ratio of boys who cast their vote for Taro is 3/5 of the whole boy and 136 girls cast their vote for Taro.
Number of girls who cast their vote for Jiro was 14 more than that of girls who cast her vote for Hanako.
Answer the following questions.
(1) Indicate the rate of the number of votes obtained of Taro, Jiro, and Hanako by the least integer.
(2) Indicate the ratio of the number of boys and girls who cast their vote for Taro by the ratio of the least integer.
(3) Find the number of all students of this junior high school.
(4) Find the number of boys who cast their vote for Hanako.
Answer
(1) 8 : 4 : 3
(2) 15 : 17
(3) 480
(4) 31
Solution
(1) The ratio of the number of votes obtained of Taro, Jiro, and Hanako is equal to the ratio of the central angle of each sector of a pie chart.
The central angle of B is 360 - (192 + 72) = 96 degrees.
Therefore, Taro : Jiro : Hanako = 192 : 96 : 72 = 8 : 4 : 3.
(2) Since the ratio of the number of boys and girls of this junior high school is 5 : 7, all the students are expressed as 5 + 7 = 12.
Moreover, the sum total of the ratio calculated by (1) and 8 + 4 + 3 = 15 are expressed as all the students' number.
Then, all the students' number is set to 60 of the least common multiple of 12 and 15.
Then the ratio of the number of boys and girls is 5 : 7 = 25 : 35.
The ratio of the number of vote obtained by Taro, Jiro, and Hanako is 8 : 4 : 3 = 32 : 16 : 12.
Since the rate of number of boys who cast their vote for Taro is 3/5 of the whole boy , the number is 25 × 3/5 = 15.
Since the number of votes obtained by Taro is 32, girls number is set to 32 - 15 = 17.
The ratio to be found is 15 : 17.
(3) Since according to (2), the ratio of girls who cast their vote for Taro is 17 and the actual number is 136 persons, all the students 60 are 136 /17 x 60 = 480 persons.
(4) The number of all the girls is 480 × (7 / 5+7) = 280.
The number of girls who voted for Jiro and Hanako in total is 280 - 136 = 144.
Because there are fewer 14 people in the number of girls who voted for Hanako than the number of girls who voted for Jiro, the number of girls who voted for Hanako is (144 - 14) / 2 = 65.
As the vote number of people of Hanako was 96 people, the number of boys to be found is 96 - 65 = 31.
A pie chart expresses the rate of the number of votes obtained by each person.
The ratio of the number of boys students and girls students of this junior high school 5 : 7.
The ratio of boys who cast their vote for Taro is 3/5 of the whole boy and 136 girls cast their vote for Taro.
Number of girls who cast their vote for Jiro was 14 more than that of girls who cast her vote for Hanako.
Answer the following questions.
(1) Indicate the rate of the number of votes obtained of Taro, Jiro, and Hanako by the least integer.
(2) Indicate the ratio of the number of boys and girls who cast their vote for Taro by the ratio of the least integer.
(3) Find the number of all students of this junior high school.
(4) Find the number of boys who cast their vote for Hanako.
Answer
(1) 8 : 4 : 3
(2) 15 : 17
(3) 480
(4) 31
Solution
(1) The ratio of the number of votes obtained of Taro, Jiro, and Hanako is equal to the ratio of the central angle of each sector of a pie chart.
The central angle of B is 360 - (192 + 72) = 96 degrees.
Therefore, Taro : Jiro : Hanako = 192 : 96 : 72 = 8 : 4 : 3.
(2) Since the ratio of the number of boys and girls of this junior high school is 5 : 7, all the students are expressed as 5 + 7 = 12.
Moreover, the sum total of the ratio calculated by (1) and 8 + 4 + 3 = 15 are expressed as all the students' number.
Then, all the students' number is set to 60 of the least common multiple of 12 and 15.
Then the ratio of the number of boys and girls is 5 : 7 = 25 : 35.
The ratio of the number of vote obtained by Taro, Jiro, and Hanako is 8 : 4 : 3 = 32 : 16 : 12.
Since the rate of number of boys who cast their vote for Taro is 3/5 of the whole boy , the number is 25 × 3/5 = 15.
Since the number of votes obtained by Taro is 32, girls number is set to 32 - 15 = 17.
The ratio to be found is 15 : 17.
(3) Since according to (2), the ratio of girls who cast their vote for Taro is 17 and the actual number is 136 persons, all the students 60 are 136 /17 x 60 = 480 persons.
(4) The number of all the girls is 480 × (7 / 5+7) = 280.
The number of girls who voted for Jiro and Hanako in total is 280 - 136 = 144.
Because there are fewer 14 people in the number of girls who voted for Hanako than the number of girls who voted for Jiro, the number of girls who voted for Hanako is (144 - 14) / 2 = 65.
As the vote number of people of Hanako was 96 people, the number of boys to be found is 96 - 65 = 31.
