Retro Rides is a club for owners of vintage cars and motorcycles. Every year the club gets together for a ride. This year, 38 vehicles participated in the ride. The total number of tires of all the vehicles was 114. Assuming each car has 4 tires and each motorcycle has 2 tires, how many each of cars and motorcycles participated in the ride? A. 16 cars; 22 motorcycles B. 23 cars; 15 motorcycles C. 19 cars; 19 motorcycles D. 21 cars; 17 motorcycles

22 cars; 32 motorcycles

Step-by-step explanation:

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C. 19 cars; 19 motorcycles

Step-by-step explanation:

Let c represent the number of cars and m represent the number of motorcycles that participated this year.

This year a total of 38 vehicles participated. So, we can write the equation as:

c + m = 38 (Equation 1)

Each car has 4 tires, so number of tires in c cars will be 4c.

Each motorcycle has 2 tires, so number of tires in m motorcycles will be 2m.

In total there were 114 tires, so we can set up the equation as:

4c + 2m = 114 (Equation 2)

From equation 1, m = 38 - c. Using this value in Equation 2, we get:

4c + 2 (38 - c) = 114

4c + 76 - 2c = 114

2c = 114 - 76

2c = 38

c = 19

Using this value in equation 1, we get:

19 + m = 38

m = 19

Thus, 19 cars and 19 motorcycles participated in the ride.