Dan, Laura, and Jane went grocery shopping. Dan spent three times as much as Laura and half as much as Jane. If they spent a total of $50 on grocies, how much did Jane spend?

Options

A. 15
B. 25
C. 30
D. 45

Answer

To solve the problem step by step, we can follow this approach:

1. **Define Variables**:
- Let \( L \) be the amount Laura spent.
- According to the problem, Dan spent three times as much as Laura, so Dan spent \( 3L \).
- It is also stated that Dan spent half as much as Jane, which means Jane spent twice as much as Dan. Therefore, Jane spent \( 2 \times (3L) = 6L \).

2. **Set Up the Equation**:
- Now, we can express the total amount spent by all three:
\[ L + 3L + 6L = 50 \]
- Simplifying this gives:
\[ 10L = 50 \]

3. **Solve for \( L \)**:
- To find \( L \), divide both sides of the equation by 10:
\[ L = \frac{50}{10} = 5 \]

4. **Calculate Jane's Spending**:
- Since we know Jane spent \( 6L \), we can substitute the value of \( L \):
\[ \text{Jane's spending} = 6L = 6 \times 5 = 30 \]

5. **Conclusion**:
- Therefore, Jane spent **$30**.