Step 1 :Find the proportion of gold medals won by each team: \(\frac{\text{gold medals}}{\text{total medals}}\)
Step 2 :Team A gold proportion: \(\frac{1}{6} = 0.1667\)
Step 3 :Team B gold proportion: \(\frac{2}{9} = 0.2222\)
Step 4 :Compare the gold proportions: Team B has a higher proportion of gold medals.
Step 5 :Find the number of gold medals won by each team: \(\text{gold proportion} \times \text{total number of medals}\)
Step 6 :Team A gold medals: \(0.1667 \times 75 = 12.5\) (round up to 13)
Step 7 :Team B gold medals: \(0.2222 \times 120 = 26.64\) (round down to 26)
Step 8 :Compare the number of gold medals: Team B has a higher number of gold medals.
Step 9 :\(\boxed{\text{a) Team B won the higher proportion of gold medals.}}\)
Step 10 :\(\boxed{\text{b) Team A won 13 gold medals, and Team B won 26 gold medals.}}\)
Step 11 :\(\boxed{\text{c) Team B won the higher number of gold medals.}}\)