Question

Which situation represents a proportional relationship?

A) Julie sold 4 necklaces for $12 and 9 necklaces for $25.
B) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.
C) Larry packed 24 apples in 6 boxes and 46 apples in 9 boxes.
D) Allie put 14 pieces of candy in 2 bags and 30 pieces of candy in 4 bags.

Answer 1

B) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y=kx`

The ratio between the two variables is a constant called constant of proportionality k

`k=y/x`

Verify each case

A) Julie sold 4 necklaces for $12 and 9 necklaces for $25.

`(4)/(12)=(9)/(25)`

Multiply in cross

`4(25)=9(12)\\100\\eq108`

Is not true

therefore

The situation not represent a proportional relationship

B) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.

`(5)/(25)=(8)/(40)`

Multiply in cross

`5(40)=8(25)\\200=200`

Is true

therefore

The situation represent a proportional relationship

C) Larry packed 24 apples in 6 boxes and 46 apples in 9 boxes

`(24)/(6)=(46)/(9)`

Multiply in cross

`24(9)=46(6)\\216\\eq276`

Is not true

therefore

The situation not represent a proportional relationship

D) Allie put 14 pieces of candy in 2 bags and 30 pieces of candy in 4 bags

`(14)/(2)=(30)/(4)`

Multiply in cross

`14(4)=30(2)\\56\\eq60`

Is not true

therefore

The situation not represent a proportional relationship