Use the table to answer the 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

1 answer

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.