# Beef, chicken or duck? So many choices

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?

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