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Kenneth and his mom spent all morning preparing cucumber sandwiches for their annual Fourth of July party! At the party, Kenneth handed out a cucumber sandwich to each kid. He also gave each of the $22$ adults a cucumber sandwich. In all, Kenneth handed out $53$ cucumber sandwiches.$\newline$Let $k$ represent the number of kids at the party. Which equation models the problem?$\newline$Choices:$\newline$$(A)$ $k - 22 = 53$$\newline$$(B)$ $k + 22 = 53$$\newline$Solve this equation to find how many kids were at the party.$\newline$$\_\_\_$ kids$\newline$