To solve this problem, let's denote:

• $x$: the number of black and white paintings.
• $y$: the number of colored paintings.

The problem states that Brian paints 9 paintings in total and spends 120 minutes painting them. This gives us two equations:

1. $x + y = 9$ (the total number of paintings)
2. $10x + 25y = 120$ (the total time spent painting)

Step 1: Solve for one variable in terms of the other

From the first equation: $y = 9 - x$

Step 2: Substitute into the second equation

Substitute $y = 9 - x$ into the second equation: $10x + 25(9 - x) = 120$

Simplify: $10x + 225 - 25x = 120$ $-15x + 225 = 120$ $-15x = -105$ $x = 7$

Step 3: Solve for $y$

Using $x + y = 9$: $7 + y = 9$ $y = 2$

Final Answer

Brian painted 7 black and white paintings and 2 colored paintings in 120 minutes.

Verification

• Time for 7 black and white paintings: $7 \times 10 = 70$ minutes.
• Time for 2 colored paintings: $2 \times 25 = 50$ minutes.
• Total time: $70 + 50 = 120$ minutes. ✅

Would you like additional details or explanations?

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Here are 5 follow-up questions:

1. How many paintings can Brian complete if he paints for 200 minutes?
2. What is the ratio of black and white to colored paintings?
3. What if Brian takes 12 minutes for black and white and 30 minutes for colored paintings? How does that affect the total?
4. How does the solution change if Brian paints 12 paintings in 120 minutes?
5. How would the equations change if Brian paints only black and white paintings?

Tip: Break problems like these into manageable steps to simplify equations and maintain accuracy!