Question

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:

A= left-handed: 42
Right-handed: 483

B= lef-handed: 28
Right-handed: 378

C= left-handed: 48
Right-handed: 504

D= left-handed: 56
Right-handed: 560

E: left-handed: 30
Right-handed: 315

Answer 1

OPTION C.

OPTION E.

Explanation:

A relationship is proportional if the ratio between the variables is always the same.

In this case we know that the numbers of left- and right-handed students at West Junior High are proportional to the numbers at East Middle School and there are 58 left-handed students and 609 right-handed students at East Middle School. Therefore, the ratio is:

`ratio=(58)/(609)=(2)/(21)`

So, we can check the ratio in each option to know which has ratio
`(2)/(21)`:

OPTION A:

`(42)/(483)=(2)/(23)`

OPTION B:

`(28)/(378)=(2)/(27)`

OPTION C:

`(48)/(504)=(2)/(21)`

OPTION D:

`(56)/(560)=(1)/(10)`

OPTION E:

`(30)/(315)=(2)/(21)`

Therefore, you can observe that the numbers of left-handed and right-handed students at West Junior High could be:

`Left-handed: 48\\Right-handed: 504\\\\\\Left-handed: 30\\Right-handed: 315`

Answer 2

C. Left-handed: 48, Right-handed: 504

D. Left-handed: 30, Right-handed: 315

Explanation:

We are given that there are 58 left-handed students and 609 right-handed students at East Middle School and these numbers of students are proportional to the number of left and right handed students at East Middle School.

Given the above information, we are are to determine which two options could be the the numbers of left-handed and right-handed students at West Junior High.

Ratio of right handed to left handed students at East Middle School =
`(609)/(58) = 10.5`

Checking for ratios of the given options:

A.
`(483)/(42) =11.5`

B.
`(378)/(28) =13.5`

C.
`(504)/(48) =10.5`

D.
`(560)/(56) =10`

E.
`(315)/(30) =10.5`

Therefore, the possible numbers of left-handed and right-handed students at West Junior High could be C. Left-handed: 48, Right-handed: 504 and D. Left-handed: 30, Right-handed: 315.