Question

Congratulations! You just won the lottery and plan to buy a bunch of cars and motorcycles for all your friends. You purchase 50 new vehicles in total. Altogether, the vehicles you purchase have a total of 164 wheels. How many of each vehicle did you purchase?

Answer 1

Step 1

Let n represent car and m represent motorcycles.

n + m = 50 ...................1

car has four wheels and motorcycle has two wheels

4n + 2m = 164 .............................. 2

Step 2

Solve equation 1 and 2 simultaneously.

from (1), make n subject of relation and substitute in equation 2.

n = 50 - m

Step 3

Substitute n in equation 2

4(50 - m) + 2m = 164

200 - 4m + 2m = 164

collect like terms

200 - 164 = 4m - 2m

36 = 2m

m = 36/2

m = 18

next find n

n = 50 - m

n = 50 - 18

n = 32

There are 32 cars and 18 motorcycles.