Question

Select all the correct answers.
Henry collects shells from the beach every day he is on vacation. Each day he collects shells, he always collects three times as many white shells as black shells. Which of these ratio statements could compare the number of white shells to black shells Henry collects in one day?
For every 15 white shells, there are 3 black shells.
For every 21 white shells, there are 7 black shells.
For every 26 white shells, there are 8 black shells.
For every 12 white shells, there are 4 black shells.
For every 27 white shells, there are 9 black shells.

Answer 1

To determine which ratio statements correctly represent the relationship between the number of white shells and black shells collected by Henry, we note that Henry collects three times as many white shells as black shells. This means that the ratio of white shells to black shells should be 3:1.

We can analyze each statement to see if it maintains this ratio:

1. **For every 15 white shells, there are 3 black shells.**
- Ratio: \( \frac{15}{3} = 5:1 \) (not correct)

2. **For every 21 white shells, there are 7 black shells.**
- Ratio: \( \frac{21}{7} = 3:1 \) (correct)

3. **For every 26 white shells, there are 8 black shells.**
- Ratio: \( \frac{26}{8} = 3.25:1 \) (not correct)

4. **For every 12 white shells, there are 4 black shells.**
- Ratio: \( \frac{12}{4} = 3:1 \) (correct)

5. **For every 27 white shells, there are 9 black shells.**
- Ratio: \( \frac{27}{9} = 3:1 \) (correct)

Based on this analysis, the correct answers are:

- For every 21 white shells, there are 7 black shells.
- For every 12 white shells, there are 4 black shells.
- For every 27 white shells, there are 9 black shells.