let

b = the number of turkey burgers

h = the number of hamburgers

Vong grilled 21 burgers at a block party

b + h = 21

He grilled the same number of pounds of turkey burgers as hamburgers. Each turkey burger weighed 1/4 pound and each hamburger weighed 1/3 pound.

(1/4)b = (1/3)h

by solving the system of equations

b + h = 21

(1/4)b = (1/3)h

we find

b = 12

h = 9

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Vong grilles 12 turkey burgers and 9 hamburgers.