Question: A garage has 60 vehicles for sale, which are all either new or second-hand.
32 of the vehicles are mopeds and the rest are cars.
8 of the mopeds are second-hand.
3 of the cars are new.
a) a) Copy and complete the frequency tree to work out the value of M.
b) In total, how many of the vehicles are second-hand?
1. **State the problem:** We have a total of $60$ vehicles, split into mopeds and cars.
- Total vehicles: $60$
- Mopeds: $32$
- Cars: $60 - 32 = 28$
- Second-hand mopeds: $8$
- New cars: $3$
We need to find:
a) The value of $M$ (which we interpret as the number of new mopeds).
b) The total number of second-hand vehicles.
2. **Frequency tree setup:**
- Mopeds: $32$ total
- Second-hand mopeds: $8$
- New mopeds: $M$
- Cars: $28$ total
- New cars: $3$
- Second-hand cars: $28 - 3 = 25$
3. **Calculate $M$:**
Since total mopeds are $32$, and second-hand mopeds are $8$, the new mopeds $M$ is:
$$M = 32 - 8 = 24$$
4. **Calculate total second-hand vehicles:**
Second-hand mopeds: $8$
Second-hand cars: $25$
Total second-hand vehicles:
$$8 + 25 = 33$$
**Final answers:**
a) $M = 24$
b) Total second-hand vehicles = $33$