1. **State the problem:** Ricky mixes white and blue paint in a ratio of 4 pints white to 12 pints blue. The total paint combined is 56 pints. We need to find how many pints are blue and how many are white.
2. **Write the ratio and total:** The ratio of white to blue paint is $4:12$, which can be simplified to $1:3$ by dividing both parts by 4.
3. **Set variables:** Let the number of white pints be $x$ and blue pints be $3x$ (since the ratio is $1:3$).
4. **Write the total equation:**
$$x + 3x = 56$$
5. **Simplify the equation:**
$$4x = 56$$
6. **Solve for $x$:**
$$x = \frac{56}{4}$$
$$x = 14$$
7. **Find the amounts:**
- White paint = $x = 14$ pints
- Blue paint = $3x = 3 \times 14 = 42$ pints
8. **Check:**
$$14 + 42 = 56$$ which matches the total paint.
**Final answer:**
- Blue pints of paint: 42
- White pints of paint: 14
Paint Ratio 381B8F
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.