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The problem asks for two equations that describe the relationship between the units of white paint, \( w \), and black paint, \( b \), that Pablo mixes.

Given:
- Pablo mixes 3 units of white paint for every 1 unit of black paint.

This describes a ratio of 3:1 between white paint and black paint. From this, we can set up the following two equations:

1. \( w = 3b \): The amount of white paint \( w \) is three times the amount of black paint \( b \).
2. \( b = \frac{w}{3} \): The amount of black paint \( b \) is one-third of the amount of white paint \( w \).

These equations represent the relationship between the two quantities based on the ratio.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. If Pablo uses 6 units of white paint, how much black paint will he need?
2. What is the total amount of paint Pablo will have if he mixes 3 units of white paint and 1 unit of black paint?
3. How would the equation change if Pablo used 2 units of black paint for every 3 units of white paint?
4. Can you express the total amount of paint as a single equation involving both \( w \) and \( b \)?
5. What happens to the ratio if Pablo adds an additional unit of white paint?

**Tip**: Ratios can often be converted into equations by using multiplication or division to maintain the relationship between the quantities.

Pablo mixes 3 units white paint and 1 unit black paint to make gray paint. What two equations show the relationship between units of white paint, w, and units of black paint, b?

Solve a problem involving the mixing of white and black paint in a 3:1 ratio. Learn how to write two equations to express the relationship between the units of white paint (w) and black paint (b). Suitable for middle school students, Grades 6-8.

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