The minimum volume of the tank required for combined lengths of the fish is \(\boxed{15\,{\text{gallons}}}\).
Further Explanation:
The graph between the capacity of the tank and the combined length of the fishes present in the tank starts from the point \(\left( {0,1} \right)\) and further it passes through the point \(\left( {3,4} \right)\).
The expression for the slope of the graph is as given below.
\(m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\)
Substitute the co-ordinates of the points in equation of slope.
\(\begin{aligned}m&= \frac{{4 - 1}}{{3 - 0}}\\&= \frac{3}{3}\\&= 1\\\end{aligned}\)
The y-intercept of the graph is \(1\).
Write the expression for the equation of line of the graph.
\(y = mx + c\)
Substitute \(1\) for \(m\) and \(1\) for \(c\) in above expression.
\(\begin{aligned}y&= \left( {1 \cdot x} \right) + 1 \hfill\\y&= x + 1 \hfill\\\end{aligned}\)
The total length of all the fishes present inside the tank is.
\(\begin{aligned}{L_{total}} &= \left( {4 \times 2} \right) + \left( {3 \times 1} \right) + \left( {1 \times 3} \right) \\&= 8 + 3 + 3\\&= 14\,{\text{inches}}\\\end{aligned}\)
Since the length of the fishes is given on the x-axis, substitute \(14\,{\text{inches}}\) for \(x\) in equation of line of the graph.
\(\begin{aligned}y&= 14 + 1\\&= 15\,{\text{gallons}}\\\end{aligned}\)
Thus, the minimum volume of the tank required for combined lengths of the fish is \(\boxed{15\,{\text{gallons}}}\).
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Answer Details:
Grade: High School
Chapter: Units and Measurements
Subject: Physics
Keywords: Aquarium, size of tank, capacity of the tank, combined lengths, the fish, platys, guppies, loach, inch, smallest capacity, gallon.
