Butcher Shop Prices

At my butcher shop, I can buy 2 pounds of chicken thigh and 1 pound of chicken feet for 738 cents, and I can buy 3 pounds of chicken thigh and 1 pound of chicken heart for 852 cents.

For how many ordered sets of integers \( (t, f, h ) \), each of which are between 0 and 100 inclusive, can I determine the exact total cost of \(t\) pounds of chicken thigh, \(f\) pounds of chicken feet and \( h \) pounds of chicken heart?

Assume that the cost per pound of any given meat is constant.

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