Beth is $b$ years old. Sam is 4 years younger than Beth. The product of their ages is 621 . a) Show that $b^{2}-4 b-621=0$. b) Work out Sam's age.

Step 1 ：\(b(b-4)=621\)

Step 2 ：\(b^{2}-4b=621\)

Step 3 ：\(b^{2}-4b-621=0\)\(\boxed{b^{2}-4b-621=0}\)

Step 4 ：\(b=23\) or \(b=-27\)

Step 5 ：Since age cannot be negative, \(b=23\)

Step 6 ：Sam's age is \(b-4=23-4=19\)

Step 7 ：\(\boxed{19}\)