Step 1 :Given that on December 13,2007 , one Chinese yuan was worth 0.14 U.S. dollars.
Step 2 :(a) To find out how many yuan 23.39 dollars is worth, we need to divide the amount in dollars by the conversion rate. So, \(\frac{23.39}{0.14} = 167.07\) yuan.
Step 3 :(b) To find out how many dollars 191.77 yuan is worth, we need to multiply the amount in yuan by the conversion rate. So, \(191.77 \times 0.14 = 26.85\) dollars.
Step 4 :Final Answer: (a) On that date, 23.39 dollars was worth \(\boxed{167.07}\) yuan. (b) On that date, 191.77 yuan was worth \(\boxed{26.85}\) dollars.