Question

A shop sells bicycles and tricycles. In total there are 77 cycles (cycles include both bicycles and tricycles) and 1919 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.

Answer 1

Let x and y be numbers of bicycles and tricycles, respectively

x + y = 7 (i)

2 x + 3 y = 19 (ii)

Multiplying (1) by 2 gives:

2 x + 2 y = 14 (iii)

Subtracting (iii) from (ii) gives:

y = 19 − 14 = 5

Substituting 5 for y in (i) gives:

x=7−5=2

Therefore there are 2 bicycles and 5 tricycles.

Explanation: