In a large aquarium, there are 3 starfish for every 4 sea horses.
(a) Write the ratio of starfish to sea horses. 0
(b) If there are 44 sea horses in the large aquarium, how many starfish are there? starfish
The Correct Answer and Explanation is :
To solve the problem, let’s break it down into two parts:
(a) Writing the Ratio of Starfish to Sea Horses
The ratio of starfish to sea horses is given as 3 starfish for every 4 sea horses. This can be expressed as:
[
\text{Ratio of Starfish to Sea Horses} = \frac{3 \text{ starfish}}{4 \text{ sea horses}}
]
This can also be written as 3:4, which shows the relationship between the two groups.
(b) Finding the Number of Starfish When There Are 44 Sea Horses
We know from the ratio that for every 4 sea horses, there are 3 starfish. We can use this information to find the number of starfish when there are 44 sea horses.
- Set up the proportion based on the ratio: [
\frac{3 \text{ starfish}}{4 \text{ sea horses}} = \frac{x \text{ starfish}}{44 \text{ sea horses}}
] Here, ( x ) represents the number of starfish we want to find. - Cross-multiply to solve for ( x ): [
3 \times 44 = 4 \times x
] This simplifies to: [
132 = 4x
] - Solve for ( x ): [
x = \frac{132}{4} = 33
]
Therefore, when there are 44 sea horses, there are 33 starfish in the aquarium.
Explanation
Understanding ratios helps in various real-world applications, such as managing the populations of species in an aquarium. The ratio of 3:4 indicates a proportional relationship, which can be scaled up or down depending on the actual numbers involved. By applying basic algebra, we set up a proportion based on the known ratio, enabling us to determine the number of starfish corresponding to a specified number of sea horses. This approach is particularly useful in scenarios where maintaining balance in ecosystems is crucial, ensuring that different species are kept in proportion to support a healthy environment.