To find out how many cups of red paint should be added to 1 cup of white paint, we first need to determine the ratio of red paint to white paint in the original mixture.
We are given the original mixture:
- 3 cups of red paint
- 7 cups of white paint
The ratio of red to white paint is: \[ \text{Ratio of red to white} = \frac{3 \text{ cups of red}}{7 \text{ cups of white}} \]
Now, we want to find out how many cups of red paint (\(x\)) should be added to 1 cup of white paint. We can set up the ratio as follows: \[ \frac{x \text{ cups of red}}{1 \text{ cup of white}} = \frac{3}{7} \]
To solve for \(x\), we cross-multiply: \[ x \cdot 7 = 3 \cdot 1 \] \[ 7x = 3 \] \[ x = \frac{3}{7} \]
Therefore, to create the same shade of pink with 1 cup of white paint, you should add \(\frac{3}{7}\) cups of red paint.