Question

leonard used 2/7 of his paycheck to pay his cell phone bill and put 1/3 of his paycheck in his savings. Based on the amount of money left,, which of the following are amounts he could spend on a new video game?

Answer 1

To determine how much Leonard has left after he paid his cell phone bill and put money into savings, we first need to find out how much of his paycheck he used for these expenses.

1. **Calculating the total fractions used:**
- Leonard used \( \frac{2}{7} \) of his paycheck for his cell phone bill.
- He also put \( \frac{1}{3} \) of his paycheck into savings.

2. **Finding a common denominator:**
- The denominators are 7 and 3.
- The least common multiple of 7 and 3 is 21.

3. **Converting the fractions:**
- For the cell phone bill:
\[
\frac{2}{7} = \frac{2 \times 3}{7 \times 3} = \frac{6}{21}
\]
- For savings:
\[
\frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}
\]

4. **Adding the fractions:**
\[
\frac{6}{21} + \frac{7}{21} = \frac{13}{21}
\]

5. **Calculating the remaining amount:**
- The total fraction of the paycheck Leonard has left after these expenses is:
\[
1 - \frac{13}{21} = \frac{21}{21} - \frac{13}{21} = \frac{8}{21}
\]

Now Leonard has \( \frac{8}{21} \) of his paycheck left.

**Identifying possible amounts for the video game:**
- To understand amounts Leonard could spend on a new video game, we can consider fractions of his paycheck that are less than or equal to \( \frac{8}{21} \).

Here are a few amounts:
- \( \frac{1}{21} \)
- \( \frac{2}{21} \)
- \( \frac{3}{21} \)
- \( \frac{4}{21} \)
- \( \frac{5}{21} \)
- \( \frac{6}{21} \)
- \( \frac{7}{21} \)
- \( \frac{8}{21} \)

Any value equal to or less than \( \frac{8}{21} \) would be a valid amount Leonard could spend on a new video game. If you have specific options to consider, please provide them so that I can help you determine which amounts are valid.