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:B) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.Step-by-step explanation:we know thatA relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y=kx[/tex]The ratio between the two variables is a constant called constant of proportionality k[tex]k=y/x[/tex]Verify each caseA) Julie sold 4 necklaces for $12 and 9 necklaces for $25.[tex]\frac{4}{12}=\frac{9}{25}[/tex]Multiply in cross[tex]4(25)=9(12)\\100\neq108[/tex] Is not truethereforeThe situation not represent a proportional relationshipB) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.[tex]\frac{5}{25}=\frac{8}{40}[/tex]Multiply in cross[tex]5(40)=8(25)\\200=200[/tex] Is truethereforeThe situation represent a proportional relationshipC) Larry packed 24 apples in 6 boxes and 46 apples in 9 boxes[tex]\frac{24}{6}=\frac{46}{9}[/tex]Multiply in cross[tex]24(9)=46(6)\\216\neq276[/tex] Is not truethereforeThe situation not represent a proportional relationshipD) Allie put 14 pieces of candy in 2 bags and 30 pieces of candy in 4 bags[tex]\frac{14}{2}=\frac{30}{4}[/tex]Multiply in cross[tex]14(4)=30(2)\\56\neq60[/tex] Is not truethereforeThe situation not represent a proportional relationship