Question

Peacock purple paint is made by mixing red paint and blue paint in the ratio 3 to 7. Let R be an unspecified number of liters of a red paint, which can vary, and let be be the corresponding number of liters of blue paint in peacock purple paint. Reason about quantities and our definition of multiplication, and use math drawings to find and explain the following types of equations.

A.) C • R=B, where C is a suitable constant.
B.) k•B=R where k is a suitable constant.

Answer 1

Two equations can express the relationship between red and blue paint to create peacock purple paint. The first is B = 7·R, and the second is R = (1/7)·B, showing the ratios needed for the mixture.

Step-by-step explanation:

To solve the problem of creating peacock purple paint by mixing red and blue paints in the ratio 3 to 7, where R represents the liters of red paint and B represents the liters of blue paint, we can establish two equations with constants that relate these quantities.

Equation A

If we take the total amount of blue paint to be 7 times that of the amount of red paint, we can represent this relationship with the following equation: B = 7 · R, where the constant C is equal to 7. This implies that for every unit of red paint, 7 units of blue paint will be needed to maintain the correct ratio of peacock purple paint.

Equation B

Conversely, if we need to find out how much red paint is needed given a certain quantity of blue paint, we would invert the ratio to represent this relationship as R = (1/7) · B, where the constant k is equal to 1/7. This equation tells us that for every one part of red paint, there should be seven parts blue paint.