Question

A mixture of purple paint contains 6 teaspons of red paint and 15 teaspons of blue paint.To make the same shade of purple using 35 teaspons of blue paint,how much red paint would you need?

Answer 1

To make the same shade of purple with 35 teaspoons of blue paint, you would need 14 teaspoons of red paint, maintaining the 2:5 red to blue paint ratio.

Step-by-step explanation:

The student asked how much red paint would be needed to mix with 35 teaspoons of blue paint to achieve the same shade of purple as a mixture that contains 6 teaspoons of red paint and 15 teaspoons of blue paint. This is a proportion problem where you keep the ratio of red to blue paint the same. The original ratio is 6 teaspoons of red to 15 teaspoons of blue, which simplifies to a ratio of 2:5. To find the amount of red paint needed for 35 teaspoons of blue paint, set up a proportion: 6/15 = x/35. Solve for x to find the amount of red paint needed:

1. Multiply both sides of the equation by 35 to isolate x on one side.
2. x = (6/15) * 35
3. Simplify and calculate x.

By solving, we find that x = 14 teaspoons of red paint are needed to maintain the same shade of purple.