Question

Whitney asked her cousins to name all the types of fish they found on a family trip to the aquarium.

1/9
reported finding a salmon.

5/7
reported finding a tuna.

1/4
reported finding a swordfish.

12/23
reported finding a whale shark.

Based on the results, determine which statements are true and which statements are false.

(5 points)
True False
Over half the cousins found a tuna.


More cousins found a salmon than a tuna.


More cousins found a whale shark than a swordfish.


More cousins found a tuna than a whale shark.


More cousins found a salmon than a swordfish.

Answer 1

To evaluate the truth of the statements based on the reported findings, we first need to calculate the total number of cousins who reported findings. We can use the common denominators of the fractions given:

1. For salmon: \( \frac{1}{9} \)
2. For tuna: \( \frac{5}{7} \)
3. For swordfish: \( \frac{1}{4} \)
4. For whale shark: \( \frac{12}{23} \)

To find a common denominator, we can use the least common multiple (LCM) of 9, 7, 4, and 23. The LCM is 126.

Now, let's convert each fraction based on the common denominator of 126.

1. For salmon:
\[
\frac{1}{9} = \frac{1 \times 14}{9 \times 14} = \frac{14}{126}
\]

2. For tuna:
\[
\frac{5}{7} = \frac{5 \times 18}{7 \times 18} = \frac{90}{126}
\]

3. For swordfish:
\[
\frac{1}{4} = \frac{1 \times 31.5}{4 \times 31.5} = \frac{31.5}{126} \quad (approx. 32)
\]
Since people must be whole, let’s convert it to the nearest whole; this is more conceptual than practical for final counts.

4. For whale shark:
\[
\frac{12}{23} = \frac{12 \times 6}{23 \times 6} = \frac{72}{126}
\]

Now we summarize the number of cousins based on the total (which we will assume is 126):

- Salmon: 14 cousins
- Tuna: 90 cousins
- Swordfish: 31 cousins (rounding to 32 for conceptual)
- Whale shark: 72 cousins

With that, let's evaluate the statements:

1. **Over half the cousins found a tuna.**
- Tuna: 90 cousins / 126 total = \( \approx 71.43\% \) => **True**

2. **More cousins found a salmon than a tuna.**
- Salmon: 14 cousins < Tuna: 90 cousins => **False**

3. **More cousins found a whale shark than a swordfish.**
- Whale shark: 72 cousins > Swordfish: 32 cousins => **True**

4. **More cousins found a tuna than a whale shark.**
- Tuna: 90 cousins > Whale shark: 72 cousins => **True**

5. **More cousins found a salmon than a swordfish.**
- Salmon: 14 cousins < Swordfish: 32 cousins => **False**

Based on this assessment:

1. **True**
2. **False**
3. **True**
4. **True**
5. **False**

So, the final answers are:
- **Over half the cousins found a tuna.** True
- **More cousins found a salmon than a tuna.** False
- **More cousins found a whale shark than a swordfish.** True
- **More cousins found a tuna than a whale shark.** True
- **More cousins found a salmon than a swordfish.** False