Final answer:
The equation for the relationship between the number of cups of blue paint, b, and red paint, r, is based on their given percentage concentrations. It can be written as b = 0.17 * (b + r) and r = 0.83 * (b + r), which can also be rearranged into a proportional relationship, b = R * r, where R is a constant representing the ratio of blue to red paint.
Step-by-step explanation:
The equation for the relationship between the number of cups of blue paint, b, and the number of cups of red paint, r, can be derived from the given percentage concentrations. Since 17% of the concentration is blue (Xblue), and assuming the total paints combined to make a specific color is a constant value, the remaining 83% must be red (Xred).
To establish the relationship, we can express the concentrations as fractions of the total mixture:
- For blue paint: b = 0.17 * (b + r)
- For red paint: r = 0.83 * (b + r)
For mathematical convenience, this equation may be rearranged to other formats, including direct and indirect proportionalities. If we replace the proportionality symbol with a constant (let's just choose R to represent our constant), we can re-write the equation as b = R * r or r = R * b, where R represents the ratio of blue paint to red paint.