Once a month Deshaun takes some of his coworkers out to a baseball game. Part A: For the game being played on May 7th, each ticket costs $18 and there are three options for parking. Deshaun is planning on taking some of his coworkers to this game, and he plans on parking in the lot that has a cost of p. If the cost for Deshaun and his coworkers is $80 with parking, write an algebraic equation of the form + = $80 to model this problem. If Deshaun ended up taking 2 coworkers with him, how much did he pay for parking? Part B: For the game being played on June 18th, each ticket costs $23 and there are three options for parking. Deshaun is planning on taking three of his coworkers to this game, and he plans on parking in the lot that has a cost of q. If the cost for Deshaun and his coworkers is $108 with parking, write an arithmetic equation of the form + __ = $108 to model this problem. How much did he pay for parking? Part C: Give a logical argument on when to use an algebraic equation versus a arithmetic equation to solve a problem.

Arithmetic and Algebraic equations differ in that arithmetic equation usually contain numbers while algebraic equations will always contain a variable.

1.)

Parking cost = p

Let the number of workers he takes along = w

The equation can be written thus :

18w + p = 80

If w = 2 ;

18(2) + p = 80

36 + p = 80

p = 80 - 36

p = $44

2.)

Parking cost = q

Let the number of workers he takes along = 3

The equation can be written thus :

23(2) + q = 108
46 + q = 108

46 + q = 108

q = 108 - 46

q = 62

Algebraic equations should be used when a variable value is involved while arithmetic equations should be used with constant values.

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