Bowl S contains only marbles. If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity. If 100 marbles were added, the bowl would be full. How many marbles are in bowl S?

Options

A. 100
B. 200
C. 250
D. 300

Answer

To solve the problem, we will follow these steps:

1. **Define the Variables**: Let \( x \) be the total number of marbles in bowl S when it is full.

2. **Set Up the First Condition**: According to the problem, if \( \frac{1}{4} \) of the marbles are removed, the bowl would be filled to \( \frac{1}{2} \) of its capacity. This can be expressed mathematically as:
\[ x - \frac{1}{4}x = \frac{1}{2}x \]
Simplifying this gives:
\[ \frac{3}{4}x = \frac{1}{2}x \]

3. **Set Up the Second Condition**: The problem also states that if 100 marbles are added, the bowl would be full. This can be expressed as:
\[ \frac{1}{2}x + 100 = x \]

4. **Solve the First Equation**: From the first equation:
\[ \frac{3}{4}x = \frac{1}{2}x \]
We can multiply both sides by 4 to eliminate the fractions:
\[ 3x = 2x \]
This simplifies to:
\[ x = 200 \]

5. **Verify with the Second Condition**: Now we will check if this value satisfies the second condition:
\[ \frac{1}{2}(200) + 100 = 200 \]
Simplifying the left side:
\[ 100 + 100 = 200 \]
This confirms that our value of \( x \) is correct.

Thus, the number of marbles in bowl S is \( \boxed{200} \).