The question states that:

• The test has 25 questions in total.
• Multiple-choice questions are worth 2 points.
• Short-answer questions are worth 4 points.
• The total score for the test is 80 points.

Let the number of multiple-choice questions be $x$ and the number of short-answer questions be $y$.

We can form two equations based on the information provided:

1. The total number of questions is 25: $x + y = 25$

2. The total score for the test is 80 points: $2x + 4y = 80$

We can now solve this system of equations to find $x$ (the number of multiple-choice questions).

Step 1: Simplify the second equation

We divide the second equation by 2 to make it simpler: $x + 2y = 40$

Step 2: Solve the system of equations

Now we have the system:

1. $x + y = 25$
2. $x + 2y = 40$

We can subtract equation 1 from equation 2: $(x + 2y) - (x + y) = 40 - 25$ $y = 15$

Now that we know $y = 15$, substitute this into equation 1: $x + 15 = 25$ $x = 10$

Thus, there are 10 multiple-choice questions and 15 short-answer questions.

Now, let's check the choices:

• B: The number of multiple-choice questions plus the number of short-answer questions is 25, which is true.

So, the correct answer is B.

Would you like a more detailed explanation on any of the steps, or do you have any questions?

Here are five related questions to explore further:

1. How would the solution change if multiple-choice questions were worth 3 points instead of 2?
2. If the number of short-answer questions was reduced by 5, how would that affect the total score?
3. What would the equations look like if the test was worth 100 points instead of 80?
4. How would the distribution of points affect the difficulty level of the test?
5. What if the total number of questions was increased to 30 while keeping the total points the same?

Tip: Solving systems of equations can often be done by substitution or elimination. Practicing both methods can help you choose the faster one depending on the problem!