Which situation best represents a proportional relationship?

a. sandra sold 2 bracelets for $3 and 3 bracelets for $6.

b. jeff ran 4 miles in 20 minutes and 6 miles in 24 minutes.

c. lamont packed 27 glasses in 9 cases and 81 glasses in 27 cases.

d. fernanda placed 8 pencils in 2 boxes and 16 pencils in 8 boxes?

For 2 variable to share a proportional relationship it should follow the equation;

y = mx

where y and x are the 2 variables and m is a constant value

directly proportional means when one variable increases or decreases the other variable too increases or decreases by the same amount.

a)

2 bracelets sold for $3

1 bracelet costs - 3/2

therefore 3 bracelets would cost 3/2 * 3 = $4.5

but the cost of 3 bracelets in this case is $6 therefore this is not a proportional relationship

b)

time taken for 4 miles - 20 minutes

time taken for 1 mile - 20/4

Therefore 6 miles time taken = 20/4 * 6 = 30 minutes

but it has taken only 24 minutes to run 6 miles therefore this is not a proportional relationship

c)

number of glasses in 9 cases - 27

glasses in 1 case - 27/9

therefore glasses in 27 cases - 27/9 * 27 = 81 glasses

in the given scenario, 81 glasses were packed in 27 cases therefore this is a proportional relationship

d)

number of pencils in 2 boxes - 8

number of pencils in 1 box - 8/2

number of pencils in 8 boxes - 8/2 * 8 = 32

however in this case only 16 pencils in 8 boxes so this too is not a proportional relationship

correct answer with a proportional relationship is C