Question

Raymond and his friend Khalil each bought a stack of books from the bookfair. Raymond bought 1 graphic novel and 4 adventure novels. Khalil bought 2 graphic novels and 5 adventure novels. Did Raymond and Khalil buy the same ratio of graphic novels to adventure novels?

Answer 1

To determine if Raymond and Khalil bought the same ratio of graphic novels to adventure novels, we can calculate the ratio for each person.

For Raymond:
- He bought 1 graphic novel and 4 adventure novels.
- The ratio of graphic novels to adventure novels for Raymond is:
\[
\text{Ratio for Raymond} = \frac{1 \text{ graphic novel}}{4 \text{ adventure novels}} = \frac{1}{4}
\]

For Khalil:
- He bought 2 graphic novels and 5 adventure novels.
- The ratio of graphic novels to adventure novels for Khalil is:
\[
\text{Ratio for Khalil} = \frac{2 \text{ graphic novels}}{5 \text{ adventure novels}} = \frac{2}{5}
\]

Now we can compare the two ratios \( \frac{1}{4} \) and \( \frac{2}{5} \).

To compare these fractions, we can find a common denominator or convert them to decimals.

1. **Finding a common denominator:**
- The least common multiple of 4 and 5 is 20.
- Converting \( \frac{1}{4} \) to a fraction with a denominator of 20:
\[
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\]
- Converting \( \frac{2}{5} \) to a fraction with a denominator of 20:
\[
\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}
\]

Now we compare \( \frac{5}{20} \) and \( \frac{8}{20} \).

Since \( \frac{5}{20} < \frac{8}{20} \), the two ratios are not the same.

2. **Converting to decimals (optional):**
- \( \frac{1}{4} = 0.25 \)
- \( \frac{2}{5} = 0.4 \)

Again, we can see from the decimal comparison that \( 0.25 < 0.4 \).

**Conclusion:** Raymond and Khalil did not buy the same ratio of graphic novels to adventure novels.