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:

  1. total number of bicycles is B  
  2. 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







You will find these sort of math puzzles in various math competitions like Perennial Math, Math Olympiad, Noetic Learning Math Contest, MathCounts, MOEMS Math Olympiad, U.S.A Mathematical Talent Search (USAMTS), Purple Comet Math, Math League, American Regions Mathematics League (ARML) & others.