# Beef, chicken or duck? So many choices

**Number Theory**Level 5

At a butcher shop, 1 pound of beef and 2 pounds of chicken costs 648 cents. 1 pound of beef and 2 pounds of duck costs 926 cents. How many ordered sets of integers \( (b, c, d)\) subject to \(0 \leq b \leq 20 ,0 \leq c \leq 20, 0\leq d \leq 20 \) are there, such that we can determine the exact total cost of \(b\) pounds of beef, \(c\) pounds of chicken and \(d\) pounds of duck using the above information?