To find out how many tablespoons of white paint are needed if there are 8 tablespoons of red paint, we can set up a proportion based on the ratio of red to white paint, which is 4 tablespoons of red to 3 tablespoons of white.
The proportion can be set up as: \[ \frac{\text{Red}}{\text{White}} = \frac{4}{3} \] When there are 8 tablespoons of red paint: \[ \frac{8}{\text{White}} = \frac{4}{3} \]
Cross-multiplying gives us: \[ 4 \times \text{White} = 3 \times 8 \] \[ 4 \times \text{White} = 24 \] \[ \text{White} = \frac{24}{4} = 6 \]
So, 6 tablespoons of white paint are needed if there are 8 tablespoons of red paint.
Next, to find out how many tablespoons of red paint are needed if there are 12 tablespoons of white paint, we use the same ratio: \[ \frac{\text{Red}}{\text{White}} = \frac{4}{3} \] When there are 12 tablespoons of white paint: \[ \frac{\text{Red}}{12} = \frac{4}{3} \]
Cross-multiplying gives us: \[ 4 \times 12 = 3 \times \text{Red} \] \[ 48 = 3 \times \text{Red} \] \[ \text{Red} = \frac{48}{3} = 16 \]
So, 16 tablespoons of red paint are needed if there are 12 tablespoons of white paint.
In summary:
- If there are 8 tablespoons of red paint, 6 tablespoons of white paint are needed.
- If there are 12 tablespoons of white paint, 16 tablespoons of red paint are needed.