Calculate the Paint Ratio: Solving for Percentages in 0.7x + 0.95(1-x) = 0.91

An employee at a paint shop creates the color purple using the colors red and blue.

The red paint costs $70 per liter, while the blue paint costs$95 per liter.

What percentage of blue and red paint are used if the price of the purple paint is $91 per liter?

To solve this problem, we'll follow these steps:

• Step 1: Set up the equation using the weighted average formula
• Step 2: Solve the equation for $x$
• Step 3: Calculate the percentage of blue and red paint

Now, let's work through each step:

Step 1: The equation for the weighted average is:
$C_p = x \cdot C_b + (1-x) \cdot C_r$

Substituting the given values:
$91 = x \cdot 95 + (1-x) \cdot 70$

Step 2: Simplify and solve for $x$:
$91 = 95x + 70 - 70x$
Combine terms:
$91 = 25x + 70$
Subtract 70 from both sides:
$21 = 25x$
Divide by 25:
$x = \frac{21}{25} = 0.84$

Step 3: $x = 0.84$ means 84% of the paint is blue:
The percentage of red paint is $1 - x = 0.16$ or 16%.

Therefore, the solution to the problem is blue: 84% red: 16%.