PUZZLE 1) BICYCLES AND TRICYCLES

Question:


BINARIES BIKES Shop has a total of 32 bicycles and tricycles for rent. The shop owner checked all 74 wheels at the beginning of the season to make sure they were in good condition.

Q: How many of them are bicycles and how many are tricycles?

Hints: Assume X for bicycles and Y for tricycles, now derive 2X+3Y=74 where as X+Y=32.

Answer:

By guessing numbers of each kind that add to 32, and calculating the number of wheels they
have, you will find that the bike shop has 22 bicycles and 10 tricycles



Solution:
As Bicycles have 2 wheels and Tricycles have 3 wheels
All the wheels must be equal to 74
So 2X+3Y=74 as One Scenario

And totals cycles are equal to 32
So X+Y=32
So from the above two 2X+3Y=74, X+Y=32
First take X+Y=32
X=32-Y

Thus substitute X = 32-Y Into 2X+3Y=74
2(32-Y)+3Y=74
64-2Y+3Y=74
-2Y+3Y=74-64
Y=10

Now substitute Y=10 In 2X+3Y=74
2X+3(10)=74
2X+30=74
2X=74-30
2X=44
X=44/2
X=22

Thus we got X=22 and Y=10 so total 32
22 Bicycles and 10 Tricycles