2/5 of the trucks have four-wheel drive, and 1/3 of the vehicles that
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05 Mar 2024, 03:15
Given:
- Total vehicles = \(15\),
- Total trucks = \(T\),
- Trucks with four-wheel drive (4WD) = \( \frac{2}{5}T \),
- Total vehicles with four-wheel drive = \( \frac{6}{5}T \),
- Other vehicles = \(15 - T\).
| Category | Trucks (\(T\)) | Other Vehicles (\(15-T\)) | Total |
|------------------|----------------|---------------------------|-------------------|
| **4WD** | \( \frac{2}{5}T \) | \( \frac{4}{5}T \) | \( \frac{6}{5}T \) |
| **Not 4WD** | \( \frac{3}{5}T \) | \( 15 - T - \frac{4}{5}T \) | \( 15 - \frac{6}{5}T \) |
| **Total** | \( T \) | \( 15 - T \) | \( 15 \) |
The correction involves ensuring mathematical expressions are correctly represented and the table accurately reflects the calculations and categorizations based on the given information.
Now, the explanation:
To find the fraction of vehicles that are trucks with four-wheel drive out of the total vehicles considered (either trucks or have four-wheel drive), we use the formula:
\[ \frac{\text{Trucks with 4WD{\text{All Trucks} + \text{All 4WD} - \text{Both Trucks and 4WD \]
Given that Trucks with 4WD = \( \frac{2}{5}T \), All Trucks = \( T \), and All 4WD = \( \frac{6}{5}T \), and acknowledging that Both Trucks and 4WD is counted in both previous counts and thus doesn't need to be subtracted separately, we can simplify the formula as:
\[ \frac{\frac{2}{5}T}{T + \frac{6}{5}T - \frac{2}{5}T} \]
This simplifies further to:
\[ \frac{\frac{2}{5}T}{\frac{9}{5}T} = \frac{2}{9} \]
So, the answer to the question is \( \frac{2}{9} \), representing the fraction of the vehicles that are trucks with four-wheel drive out of the total vehicles considered.
Thanks!