Simple Algebra Equations – Cars & Bicycles

There are bicycles & cars in a parking lot. On counting, there are 36 wheels in total. Each bicycle has 1 seat & each car has 4 seats. The total number of seats upon counting was 32. Find out the number of bicycles & cars in the parking lot.

Solving:

Let’s note the clues in a logical order:

1. Each bicycle has 2 wheels & 1 seat
2. Each car has 4 wheels & 4 seats
3. Total wheels in parking lot is 36
4. Total seats in the parking lot is 32

Let us assume that in the parking lot:

5. total number of bicycles is B  
6. total number of cars is C

Here B & C are variables (or unknowns) to help us solve the problem. (You can also assume them to be any other variables like x & y.)

Since there are 2 unknowns, we need to build 2 equations from the clues marked 1, 2, 3 & 4.

Let’s look at clues (3):

(wheels on a bicycle * number of bicycles) + (wheels on a car * number of cars) = Total number of wheels 

So, from (3): 

(2 * B) + (4 * C) = 36

=> 2B + 4C = 36

Simplifying this by dividing both sides by 2, we get: 

B + 2C = 18 ————- lets label this equation as number (7)

Now let us look at clue (4):

(seat on 1 bicycle * number of bicycles) + (seats in 1 car * number of cars) = Total number of seats

So, from (4): 

(1 * B) + (4 * C) = 32

⇒ B + 4C = 32 ——– lets label this equation as number (8)

Now that we have 2 equations from the clues, we can proceed to solve the problem with equations (7) & (8).

Subtracting (7) from (8):

(B + 4C) – (B + 2C) = 32 – 18

=> B + 4C – B – 2C = 14

=> 2C = 14

=> C = 7 

So the number of Cars in the parking lot is 7

Substituting the value of C in equation (7):

B + 2C = 18

=> B = (18 – 2C)

=> B = (18 – 2*7)

=> B = (18 – 14)

=> B = 4

So the number of Bicycles in the parking lot is 4

Answer: Bicycles is 4 & Cars is 7