Rebecca is playing her favorite video game, Starlight: The Space Explorer. On the first level, she earned 3 energy points and 8 stars. On the second level, she earned 2 energy points and 5 stars. Did Rebecca earn the same ratio of energy points to stars on both levels?

Answer 1

To determine if Rebecca earned the same ratio of energy points to stars on both levels, we can calculate the ratios for each level and compare them.

For the first level:

• Energy points earned: 3
• Stars earned: 8

The ratio of energy points to stars for the first level is: \[ \text{Ratio} = \frac{\text{Energy points}}{\text{Stars}} = \frac{3}{8} \]

For the second level:

• Energy points earned: 2
• Stars earned: 5

The ratio of energy points to stars for the second level is: \[ \text{Ratio} = \frac{\text{Energy points}}{\text{Stars}} = \frac{2}{5} \]

Now we compare \(\frac{3}{8}\) and \(\frac{2}{5}\). To do this, we can find a common denominator or convert them to decimal form.

Finding a common denominator: The least common multiple of 8 and 5 is 40. We can convert both ratios.

For \(\frac{3}{8}\): \[ \frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40} \]

For \(\frac{2}{5}\): \[ \frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40} \]

Now we can compare:

• First level ratio: \(\frac{15}{40}\)
• Second level ratio: \(\frac{16}{40}\)

Since \( \frac{15}{40} \neq \frac{16}{40} \), the ratios are not equal.

Thus, Rebecca did not earn the same ratio of energy points to stars on both levels.