Question

A certain shade of pink is created by adding 3 cups of red paint to 7 cups of white paint. How many cups of red paint should be added to 1 cup of white paint? What is the constant of proportionality?

a) Cups of white paint: 1; Cups of red paint: 7/3; Constant of proportionality: 3/7
b) Cups of white paint: 1; Cups of red paint: 3/7; Constant of proportionality: 7/3
c) Cups of white paint: 1; Cups of red paint: 3; Constant of proportionality: 7
d) Cups of white paint: 1; Cups of red paint: 7; Constant of proportionality: 3

Answer 1

For every 1 cup of white paint, 3/7 cups of red paint are needed to maintain the same shade of pink. The constant of proportionality in this scenario is 3/7.

Step-by-step explanation:

To find out how many cups of red paint should be added to 1 cup of white paint to maintain the same shade of pink, we need to set up a ratio. The original mixture was 3 cups of red paint to 7 cups of white paint. This ratio must stay consistent for any amount of paint we mix.

We can write this as a proportion: 3/7 = x/1, where x is the amount of red paint needed for 1 cup of white paint. Solving this proportion by cross-multiplying gives us 3 = 7x, which simplifies to x = 3/7. Therefore, for every 1 cup of white paint, 3/7 cups of red paint are needed to achieve the same shade of pink.

The constant of proportionality is the value that relates the two quantities in a proportional relationship. Here, it is 3/7, which means for every 1 unit of white paint, 3/7 units of red paint are added.