Use the table to answer the question.

Question

White Red
3 4
x
8
9 12
12 y

The ratio of red to white paint to make the perfect color pink is 4 tablespoons of red paint to 3 tablespoons of white paint. How many tablespoons of white paint are needed if there are 8 tablespoons of red paint? How many tablespoons of red paint are needed if there are 12 tablespoons of white paint?(1 point)
White Red
3 4
8
9 12
12

Answer 1

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.