Math problem problem algebra

Question

Bobby sold 33 bikes with a total of 54 wheels, how many 3 wheel bikes and how many 2 wheel bikes did he sell?

Answer 1

Quick method is to formulate two equations in two unknowns:

Let x = number of two wheel bikes sold

and y = number of three wheel bikes sold

Using number of bikes sold:

x + y = 33

Using number of total wheels information:

2x + 3y = 54

One approach to solve:

2x + 2y = 66 (top equation multiplied by 2)

2x + 3y = 54 <<< Subtract this

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0x - y = 12 <<< This means -12 three-wheel bikes were sold, that makes no sense.

There is no solution.

In fact, looking at the problem, even if all 33 bikes were two wheelers, he'd have sold 66 wheels, so unless the number of wheels is 66 or more, no solution exists.