To change the ratio of red to blue paint in Molly's current bucket from 3:7 to 2:3, she needs to add some red paint. Here's how you can calculate the amount of red paint she should add:
1. Determine the current amount of red and blue paint in the bucket:
- Since the bucket contains 5 gallons of purple paint, the amount of red paint is 30% of 5 gallons, which is 0.3 * 5 = 1.5 gallons.
- The amount of blue paint is 70% of 5 gallons, which is 0.7 * 5 = 3.5 gallons.
2. Calculate the desired amount of red and blue paint based on the 2:3 ratio:
- Since the ratio of red to blue paint is 2:3, let's assume the total amount of paint needed to achieve this ratio is x gallons.
- According to the ratio, the amount of red paint should be 2/5 * x gallons, and the amount of blue paint should be 3/5 * x gallons.
3. Set up an equation to find the value of x:
- The total amount of paint needed (x) is equal to the sum of the current amount of red paint (1.5 gallons) and the desired amount of red paint (2/5 * x gallons): x = 1.5 + (2/5 * x).
- Simplify the equation: 1.5 = (2/5 * x) - x/5.
4. Solve the equation for x:
- Multiply both sides of the equation by 5 to eliminate the fraction: 7.5 = 2x - x.
- Combine like terms: 7.5 = x.
- Therefore, the total amount of paint needed to achieve the desired ratio is 7.5 gallons.
5. Calculate the amount of red paint to add:
- The amount of red paint to add is 2/5 * 7.5 gallons = 3 gallons.
So, Molly should add 3 gallons of red paint to her current 5-gallon bucket of purple paint to achieve the desired ratio of red to blue paint of 2:3.