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
Accepted Solution
A:
Answer:C. 19 cars; 19 motorcyclesStep-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) = 1144c + 76 - 2c = 1142c = 114 - 762c = 38c = 19Using this value in equation 1, we get:19 + m = 38m = 19Thus, 19 cars and 19 motorcycles participated in the ride.