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
