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

The ratio of red paint to blue paint in the original mixture is:

\[
\frac{\text{Red}}{\text{Blue}} = \frac{6}{15}
\]

To simplify this ratio:

\[
\frac{6}{15} = \frac{2}{5}
\]

This means for every 5 teaspoons of blue paint, 2 teaspoons of red paint are used.

Now, we are asked to find how much red paint is needed when using 35 teaspoons of blue paint. Since the ratio is \( \frac{2}{5} \), we can set up the proportion:

\[
\frac{2}{5} = \frac{x}{35}
\]

To solve for \( x \), the amount of red paint, we cross-multiply:

\[
2 \times 35 = 5 \times x
\]

\[
70 = 5x
\]

Now, solve for \( x \):

\[
x = \frac{70}{5} = 14
\]

So, you would need **14 teaspoons of red paint**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the amount of red paint change if you used 50 teaspoons of blue paint?
2. What if the ratio of red to blue paint changed to \( 1:3 \)?
3. How much paint would you need in total to make 10 liters of this purple paint?
4. How would the mixture change if you doubled the amount of both red and blue paint?
5. If 5 teaspoons of yellow paint were added, how would the color be affected?

**Tip**: Always reduce ratios to their simplest form before solving proportion problems!

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

This step-by-step guide shows how to solve a proportion problem involving paint mixtures. Learn how to calculate the amount of red paint needed when the blue paint quantity changes, based on the ratio 2:5. Ideal for students in Grades 6-8.

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