372 people are working in a large store. There are 4 times as many stock people as checkers, and 18 more checkers than managers. How many stock people are in the company? How many checkers? How many managers?

1) Example of “algebraic” solution:

M + S + C = 372

4C = S

M +18 = C

(C – 18) + 4C + C = 372

=>6C -18 = 372

=>6C = 390

=>C = 65

4(65) = S

=>260 = S

M + 18 = 65

=>M = 47

(This problem could be solved arithmetically with a guess and check method)

2) Example of “arithmetic” solution:

F = 120 + 30 = 150

B = 150 / 2 = 75

(Guess and check would also serve as a arithmetic solution strategy for this problem)

Example of “algebraic” solution:

120 + B + F = 345

2B = F

F – 30 = 120

120 + B + 2B = 345

=>3B = 225

=>B = 75

When solving word problems, some students automatically apply algebraic methods that are unnecessarily cumbersome. Other students refuse to use algebraic methods (relying solely on arithmetic calculations) because they do not see the utility of using algebra. These problems help assess student’s ability to flexibly apply arithmetic and algebraic solution strategies.