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

Question

1/9 reported finding a salmon.
5/7 reported finding a tuna.
1/4 reported finding a whale shark.
Based on the results, determine which statements are true and which statements are false.

Over half the cousins found a tuna. true or false
More cousins found a salmon than a tuna. true or false
More cousins found a whale shark than a swordfish. true or false
More cousins found a tuna than a whale shark. true or false
More cousins found a salmon than a swordfish. true or false

Answer 1

To determine the truth of each statement, we'll start by defining the number of cousins and using their fractions based on that number.

Let's say there are \( N \) cousins.

• For salmon: \( \frac{1}{9}N \) reported finding a salmon.
• For tuna: \( \frac{5}{7}N \) reported finding a tuna.
• For whale shark: \( \frac{1}{4}N \) reported finding a whale shark.

Now, we can analyze each statement:

1. Over half the cousins found a tuna.

   • For this to be true, \( \frac{5}{7}N \) needs to be greater than \( \frac{1}{2}N \).
   • Since \( \frac{5}{7} > \frac{1}{2} \), this is true.

2. More cousins found a salmon than a tuna.

   • This compares \( \frac{1}{9}N \) and \( \frac{5}{7}N \).
   • Since \( \frac{1}{9} < \frac{5}{7} \), this is false.

3. More cousins found a whale shark than a swordfish.

   • No data on swordfish is given, so we can't compare.
   • This statement can't be evaluated, but we can say it is not determinable (not true or false based on given data).

4. More cousins found a tuna than a whale shark.

   • This compares \( \frac{5}{7}N \) and \( \frac{1}{4}N \).
   • Since \( \frac{5}{7} > \frac{1}{4} \), this is true.

5. More cousins found a salmon than a swordfish.

   • Again, we have no data on swordfish, so we can't assess this.
   • This, too, is not determinable.

In summary:

1. True
2. False
3. Not determinable
4. True
5. Not determinable