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------------------------------------------------ A math test has 25 problems. Some are worth 2 points, and some are worth 3 points. The test is worth 60 points in total. Which system of equations can be used to determine the number of 2-point problems and the number of 3-point problems on the test?

(A) [tex]$\left\{\begin{array}{l}x+y=25 \\ 2x+3y=60\end{array}\right.$[/tex]

(B) [tex]$\left\{\begin{array}{l}x+y=60 \\ 2x+3y=25\end{array}\right.$[/tex]

(C) [tex]$\left\{\begin{array}{l}x-y=25 \\ 2x+3y=60\end{array}\right.$[/tex]

(D) [tex]$\left\{\begin{array}{l}x-y=60 \\ 2x-3y=25\end{array}\right.$[/tex]

To solve this problem, we need to find a system of equations that accurately describes the situation given in the question. Let's break it down:

1. Understanding the components:
- We have a total of 25 problems.
- Some problems are worth 2 points each.
- Some problems are worth 3 points each.
- The total number of points for the test is 60.

2. Defining the variables:
- Let [tex]$ x $[/tex] represent the number of 2-point problems.
- Let [tex]$ y $[/tex] represent the number of 3-point problems.

3. Setting up the equations:
- The total number of problems is 25, so:
[tex]\[
x + y = 25
\][/tex]
- The total number of points is 60, so:
[tex]\[
2x + 3y = 60
\][/tex]

Now, let's look at the options provided to find the system that matches these equations:
- Option (A):
[tex]\[
\left\{
\begin{array}{l}
x + y = 25 \\
2x + 3y = 60
\end{array}
\right.
\][/tex]
This system matches our equations perfectly.

- Option (B):
[tex]\[
\left\{
\begin{array}{l}
x + y = 60 \\
2x + 3y = 25
\end{array}
\right.
\][/tex]
This option swaps the roles of total points and total problems, which does not match our situation.

- Option (C):
[tex]\[
\left\{
\begin{array}{l}
x - y = 25 \\
2x + 3y = 60
\end{array}
\right.
\][/tex]
The first equation in this set does not reflect the total number of problems correctly.

- Option (D):
[tex]\[
\left\{
\begin{array}{l}
x - y = 60 \\
2x - 3y = 25
\end{array}
\right.
\][/tex]
Both equations in this option do not represent the given conditions correctly.

The correct system is Option (A), which uses the equations:
[tex]\[
x + y = 25
\][/tex]
[tex]\[
2x + 3y = 60
\][/tex]

This system will accurately help determine the number of 2-point problems and 3-point problems on the test.