At East Middle School, there are 58 left-handed students and 609 right-handed students. The numbers of left- and right-handed students at West Junior High are proportional to the numbers at East Middle School. Which of the following could be the numbers of left-handed and right-handed students at West Junior High? CHOOSE 2 ANSWERS: (Choice A) Left-handed: 42 Right-handed: 483 (Choice B) Left-handed: 28 Right-handed: 378 (Choice C) Left-handed: 48 Right-handed: 504 (Choice D) Left-handed: 56 Right-handed: 560 (Choice E) Left-handed: 30 Right-handed: 315
Answers
Answer:
Choice c and d
Step-by-step explanation:
Given: At East Middle School, there are 58 left-handed students and 609 right-handed students. The numbers of left- and right-handed students at West Junior High are proportional to the numbers at East Middle School.
To find: Out of the five given options, which two can be the numbers of right and left handed students at West Junior High.
(Choice A) Left-handed: 42 Right-handed: 483 (Choice B) Left-handed: 28 Right-handed: 378 (Choice C) Left-handed: 48 Right-handed: 504 (Choice D) Left-handed: 56 Right-handed: 560 (Choice E) Left-handed: 30 Right-handed: 315
Explanation: At East Middle School, there are 58 left and 609 right handed students.
Taking their ratio:
58/ 609
Dividing the numerator and denominator by 29, we get the ratio as- 2:21
Since it is given that the students in West Junior have the same proportion, we check the every option for the same ratio.
(Choice A) Left-handed: 42 Right-handed: 483
The ratio here becomes- 42/ 483
Dividing the numerator and denominator by 21, we get the ratio as- 2:23
(Choice B) Left-handed: 28 Right-handed: 378
The ratio here becomes- 28/ 378
Dividing the numerator and denominator by 14, we get the ratio as- 2:27
(Choice C) Left-handed: 48 Right-handed: 504
The ratio here becomes- 48/ 504
Dividing the numerator and denominator by 24, we get the ratio as- 2:21
(Choice D) Left-handed: 56 Right-handed: 560
The ratio here becomes- 56/560
Dividing the numerator and denominator by 28, we get the ratio as- 2:20
(Choice E) Left-handed: 30 Right-handed: 315
The ratio here becomes- 30/315
Dividing the numerator and denominator by 15, we get the ratio as- 2:21
We observe that Choice C and Choice E have the same ratio 2:21.
Therefore, the numbers of left handed and right handed students at West Junior High can be (Choice C) Left-handed: 48 Right-handed: 504 and (Choice E) Left-handed: 30 Right-handed: 315.