Question

You want to set up an aquarium and need to determine what size tank to buy. The graph shows tank sizes using a rule that relates the capacity of the tank to the combined lengths of the fish it can hold.
If you want four 2-inch platys, three 1-inch guppies, and a 3-inch loach, what is the smallest capacity tank you can buy?

17-gallon tank
13-gallon tank
15-gallon tank
14-gallon tank

Answer 1

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 $\boxed{15\,{\text{gallons}}}$.

Learn More:

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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.

Answer 2

connexus unit 8 lesson 1 PRACTICE!

1) B

2) C

3) A

4) C

5) B

6) A

7) D  

8) A

9) D  

10) A

11) A

12) C

13) D

14) C

15) B

16) B

Hope this helps you guys out!