Question
Noah wants his boat to sail along on an even keel. The boat is divided down the middle, and on each deck the animals on the left exactly balance those on the right - all but the third deck. Can you figure out how many SEA LIONS are needed in place of the question mark so that they (and the bear) will exactly balance the six zebras?
Answers
GPT-4o mini
To find out how many sea lions are needed to balance the six zebras along with the bear, we first need to establish a way to represent the weights of these animals and understand what “exactly balance” means in this context.
Given that we need to balance the weight of the sea lions (denoted as \( S \)) plus the weight of the bear (denoted as \( B \)) against the weight of the six zebras, we can mathematically express this balance as:
\[
\text{Weight of Sea Lions} + \text{Weight of Bear} = \text{Weight of Zebras}
\]
Assuming the total weight of six zebras is \( 6Z \) (where \( Z \) equals the weight of one zebra), we need to find the total weight of the sea lions and the bear that will equal this amount.
So we can express the equation as follows:
\[
n \cdot S + B = 6Z
\]
Where \( n \) is the number of sea lions. Rearranging the equation, we have:
\[
n \cdot S = 6Z - B
\]
To determine \( n \), we would require both the weight of the bear \( B \) and the weight of the sea lions \( S \). Since we don’t have actual weight values for \( B \) or \( S \), we can't calculate an exact number without those weights.
However, if we assume we know the weight of each zebra, the sea lion, and the bear, we can compute a specific number of sea lions required. Let’s take a hypothetical but illustrative approach.
For instance, if we hypothesized:
- \( Z = 100 \text{ lbs (weight of a zebra)} \)
- \( B = 200 \text{ lbs (weight of a bear)} \)
- \( S = 50 \text{ lbs (weight of a sea lion)} \)
Plugging in the values:
\[
6Z = 6 \cdot 100 = 600 \text{ lbs}
\]
Substituting the bear’s weight:
\[
n \cdot 50 + 200 = 600
\]
Rearranging gives:
\[
n \cdot 50 = 600 - 200
\]
\[
n \cdot 50 = 400
\]
Thus, solving for \( n \):
\[
n = \frac{400}{50} = 8
\]
Therefore, in this hypothetical scenario, 8 sea lions would be needed to replace the question mark to balance out the six zebras and the bear.
If you have concrete values for the weights of a bear and sea lions, please input them into this formula to arrive at your specific answer.
Given that we need to balance the weight of the sea lions (denoted as \( S \)) plus the weight of the bear (denoted as \( B \)) against the weight of the six zebras, we can mathematically express this balance as:
\[
\text{Weight of Sea Lions} + \text{Weight of Bear} = \text{Weight of Zebras}
\]
Assuming the total weight of six zebras is \( 6Z \) (where \( Z \) equals the weight of one zebra), we need to find the total weight of the sea lions and the bear that will equal this amount.
So we can express the equation as follows:
\[
n \cdot S + B = 6Z
\]
Where \( n \) is the number of sea lions. Rearranging the equation, we have:
\[
n \cdot S = 6Z - B
\]
To determine \( n \), we would require both the weight of the bear \( B \) and the weight of the sea lions \( S \). Since we don’t have actual weight values for \( B \) or \( S \), we can't calculate an exact number without those weights.
However, if we assume we know the weight of each zebra, the sea lion, and the bear, we can compute a specific number of sea lions required. Let’s take a hypothetical but illustrative approach.
For instance, if we hypothesized:
- \( Z = 100 \text{ lbs (weight of a zebra)} \)
- \( B = 200 \text{ lbs (weight of a bear)} \)
- \( S = 50 \text{ lbs (weight of a sea lion)} \)
Plugging in the values:
\[
6Z = 6 \cdot 100 = 600 \text{ lbs}
\]
Substituting the bear’s weight:
\[
n \cdot 50 + 200 = 600
\]
Rearranging gives:
\[
n \cdot 50 = 600 - 200
\]
\[
n \cdot 50 = 400
\]
Thus, solving for \( n \):
\[
n = \frac{400}{50} = 8
\]
Therefore, in this hypothetical scenario, 8 sea lions would be needed to replace the question mark to balance out the six zebras and the bear.
If you have concrete values for the weights of a bear and sea lions, please input them into this formula to arrive at your specific answer.