Question

Retro Rides is a club for owners of vintage cars and motorcycles. Every year the club gets together for a ride. This year, 53 vehicles participated in the ride. The total number of tires of all the vehicles was 148. Assuming each car has 4 tires and each motorcycle has 2 tires, how many each of cars and motorcycles participated in the ride?

Answer 1

21 cars, 32 motorcycles.
create a system of equations using x for cars and y for motorcycles.
$\left \{ {{x+y=53} \atop {4x+2y=148}} \right.$
multiply the top equation by 2 to prepare for elimination method
$\left \{ {{2x+2y=106} \atop {4x+2y=148}} \right.$
subtract terms
$\left \{ {{2x+2y=106} \atop {-4x-2y=-148}} \right. = (-2x = -42)$
divide both sides by negative 2 to solve for x
x =21
plug in x  into original equation to solve for y.
21 + y = 53
subtract both sides by 21
y=32