Mary has d dollars to spend and goes on a shopping spree . First she spends `2/5` of her money on shoes . Then she spends `3/4` of what's left on a few books. Finally she buys a raffle ticket that costs `1/3` of her remaining dollars. What fraction of d is left ?

Options

A. `1/10`
B. `3/20`
C. `1/5`
D. `3/10`

Answer

To solve the problem step by step, let's break down Mary's spending:

1. **Initial Amount**: Mary starts with \( d \) dollars.

2. **Spending on Shoes**:
- Mary spends \( \frac{2}{5} \) of her money on shoes.
- Amount spent on shoes:
\[ \text{Amount on shoes} = \frac{2}{5}d \]
- Remaining amount after buying shoes:
\[ \text{Remaining} = d - \frac{2}{5}d = \frac{3}{5}d \]

3. **Spending on Books**:
- Mary then spends \( \frac{3}{4} \) of the remaining amount on books.
- Amount spent on books:
\[ \text{Amount on books} = \frac{3}{4} \times \frac{3}{5}d = \frac{9}{20}d \]
- Remaining amount after buying books:
\[ \text{Remaining} = \frac{3}{5}d - \frac{9}{20}d \]

To subtract these fractions, we need a common denominator. The common denominator of 5 and 20 is 20:
\[ \frac{3}{5}d = \frac{12}{20}d \]
Now, subtract:
\[ \text{Remaining} = \frac{12}{20}d - \frac{9}{20}d = \frac{3}{20}d \]

4. **Buying a Raffle Ticket**:
- Mary buys a raffle ticket that costs \( \frac{1}{3} \) of her remaining dollars.
- Amount spent on the raffle ticket:
\[ \text{Amount on raffle ticket} = \frac{1}{3} \times \frac{3}{20}d = \frac{1}{20}d \]
- Remaining amount after buying the raffle ticket:
\[ \text{Remaining} = \frac{3}{20}d - \frac{1}{20}d = \frac{2}{20}d = \frac{1}{10}d \]

5. **Final Answer**:
- The fraction of \( d \) that is left is:
\[ \frac{1}{10}d \]

Thus, the fraction of \( d \) that is left is \( \frac{1}{10} \).