To determine 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 given ratio of red to white paint (4 tablespoons of red to 3 tablespoons of white).
Using the ratio:
\[ \frac{\text{Red}}{\text{White}} = \frac{4}{3} \]
Let \( x \) be the amount of white paint needed when there are 8 tablespoons of red paint. We can set up the proportion:
\[ \frac{8}{x} = \frac{4}{3} \]
Cross-multiplying gives:
\[ 4x = 8 \times 3 \] \[ 4x = 24 \] \[ x = 6 \]
So, if there are 8 tablespoons of red paint, we need 6 tablespoons of white paint.
Now, for the second part, to determine how many tablespoons of red paint are needed if there are 12 tablespoons of white paint, we can again use the same ratio.
Using the ratio:
\[ \frac{\text{Red}}{\text{White}} = \frac{4}{3} \]
Let \( y \) be the amount of red paint needed when there are 12 tablespoons of white paint. We can set up the proportion:
\[ \frac{y}{12} = \frac{4}{3} \]
Cross-multiplying gives:
\[ 3y = 4 \times 12 \] \[ 3y = 48 \] \[ y = 16 \]
So, if there are 12 tablespoons of white paint, we need 16 tablespoons of red paint.
Final Answers:
- 6 tablespoons of white paint for 8 tablespoons of red paint.
- 16 tablespoons of red paint for 12 tablespoons of white paint.
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