To solve the problem, we set up the following equations:

Variables

• Let $x$ be the number of black-and-white paintings.
• Let $y$ be the number of colored paintings.

Constraints

1. The total number of paintings is $9$:
   $x + y = 9$

2. The total time to paint all the paintings is $120$ minutes:
   $15x + 25y = 120$

Solve the System of Equations

From equation (1): $y = 9 - x$

Substitute $y = 9 - x$ into equation (2): $15x + 25(9 - x) = 120$

Simplify: $15x + 225 - 25x = 120$ $-10x + 225 = 120$ $-10x = -105$ x = 10.5 \quad \text{(not valid as x$$ must be an integer)}. ]

Hence It seems there is no integer solution to satisfy the conditions with the provided information. Let me revise the setup or clarify constraints.Let’s re-evaluate carefully:

Variables

• Let $x$ represent the number of black-and-white paintings.
• Let $y$ represent the number of colored paintings.

Constraints

1. The total number of paintings is $9$: [ x + y = 9$$

2. The total time to paint all the paintings is $120$ minutes: $15x + 25y = 120$

Solving the System of Equations

From equation (1): $y = 9 - x$

Substitute $y = 9 - x$ into equation (2): $15x + 25(9 - x) = 120$

Simplify: $15x + 225 - 25x = 120$ $-10x + 225 = 120$ $-10x = -105$ $x = 10.5$

Since $x$ and $y$ must be integers, there may be an inconsistency with the constraints or interpretation. Would you like to clarify or adjust the constraints, such as adding fractional times for paintings? Let me know!