Bikes, Trikes and Scooters
In the store there are, in
total: 36 handlebars, 24 seats, and 79 wheels.
Question: How many
of each type of cycle are there?
Answer:
Given:
In the store, there are:
- 36 handlebars
- 24 seats
- 79 wheels
We want to find how many of each type of cycle there are:
- Tricycles (3 wheels, 1 seat, 1 handlebar)
- Bicycles (2 wheels, 1 seat, 1 handlebar)
- Scooters (2 wheels, no seat, 1 handlebar)
---
Step‑by‑Step
Reasoning
1. Handlebars = Total number of cycles
Every cycle has exactly one handlebar.
So there are 36 cycles total.
---
2. Minimum wheels needed
Every cycle has at least 2 wheels.
36 x 2 = 72 wheels
But the store has 79 wheels, which is 7 extra wheels.
Those extra wheels must belong to tricycles.
So: Tricycles = 7
---
3. Seats = bicycles + tricycles
Only bicycles and tricycles have seats.
We know:
Seats = 24
Tricycles already account for 7 seats, so bicycles must account for the
remaining:
24 - 7 = 17
Bicycles = 17
---
4. Scooters = cycles with no seat
Total cycles: 36
Cycles with seats (bicycles + tricycles):17 + 7 = 24
36 - 24 = 12
Scooters = 12
---
✔ Final Answer
- 7 tricycles
- 17 bicycles
- 12 scooters
