Question

In a large aquarium, there are 7 starfish for every 5 sea horses.
(a) Write the ratio of starfish to sea horses.
(b) If there are sea horses in the large aquarium, how many starfish are there?

Answer 1

(a) The ratio of starfish to sea horses is given as 7 starfish for every 5 sea horses. This can be written as:

\[ \text{Ratio of starfish to sea horses} = 7:5 \]

(b) If we denote the number of sea horses as \( x \), we know that the ratio of starfish to sea horses is maintained at 7:5. This means that for every 5 sea horses, there are 7 starfish.

To find the number of starfish when there are \( x \) sea horses, we can set up a proportion based on the ratio:

\[
\frac{\text{Starfish}}{\text{Sea Horses}} = \frac{7}{5}
\]

Let \( s \) be the number of starfish. Then we can write the equation:

\[
\frac{s}{x} = \frac{7}{5}
\]

To solve for \( s \), we can cross-multiply:

\[
5s = 7x
\]

Now, solving for \( s \):

\[
s = \frac{7x}{5}
\]

Thus, the number of starfish in terms of the number of sea horses \( x \) is \( \frac{7x}{5} \).