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

Answer:

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

Step-by-step 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.

$\frac{4}{12}=\frac{9}{25}$

Multiply in cross

$4(25)=9(12)\\100\neq108$

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.

$\frac{5}{25}=\frac{8}{40}$

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

$\frac{24}{6}=\frac{46}{9}$

Multiply in cross

$24(9)=46(6)\\216\neq276$

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

$\frac{14}{2}=\frac{30}{4}$

Multiply in cross

$14(4)=30(2)\\56\neq60$

Is not true

therefore

The situation not represent a proportional relationship