A Garage contains only motorcycles and Cars. On Tuesday, the total number of…

Step-by-Step Solution

To determine the possible number of motorcycles, we can model the situation with a linear equation based on the wheel counts of the vehicles.

1. Define the variables:

   • Let x be the number of motorcycles. Since a motorcycle has 2 wheels, the total wheels from motorcycles is 2x.

   • Let y be the number of cars. Since a car has 4 wheels, the total wheels from cars is 4y.

2. Set up the equation:

   • The total number of wheels is 266: 2x + 4y = 266

3. Simplify the equation:

   • Dividing the entire equation by 2: x + 2y = 133

4. Analyze for integer solutions:

   • Rearrange to solve for x: x = 133 - 2y

   • Since 2y is always even and 133 is odd, x must be an odd integer for y to be an integer (assuming a non-negative number of cars).

   • We check the provided options to see which value is an odd number:

     • Option A: 24 (Even)

     • Option B: 22 (Even)

     • Option C: 27 (Odd)

     • Option D: 26 (Even)

Only 27 is an odd number that satisfies the equation x + 2y = 133 where y is a non-negative integer (specifically, if x=27, then 2y = 133 - 27 = 106, so y=53).