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 104. Assuming each car has 4 tires and each motorcycle has 2 tires, how many each of cars and motorcycles participated in the ride?A. 18 cars; 20 motorcycles B. 14 cars; 24 motorcycles C. 11 cars; 27 motorcycles D. 16 cars; 22 motorcycles

Accepted Solution

Answer: OPTION BStep-by-step explanation: Let's call: c: the number of cars. m: the number of motorcycles. Based on the given information, you can set up the following system of equations: [tex]\left \{ {{c+m=38} \atop {4c+2m=104}} \right.[/tex] You can solve it by the Elimination method: - Multiply the first equation by -4. - Add both equations to cancel out the variable "c". - Solve for "m": [tex]\left \{ {(-4)(c+m)=38(-4)} \atop {4c+2m=104}} \right.\\\\\left \{ {-4c-4m=-152} \atop {4c+2m=104}} \right.\\-------\\-2m=-48\\m=24[/tex] (24 motorcycles) Β - Substitute m=24 into any of the original equations ans solve for "c". Then: [tex]c+24=38\\c=38-24\\c=14[/tex] (14 cars)