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 three 2-in. goldfish, five 1-in. guppies, and a 3-in. loach, what is the smallest capacity tank you can buy?


Notice, with 0 fish, the tank still has 4 gallons of water

Answer 1

Answer:22 gallons

Explanation:

Answer 2

18 gallons

Explanation:

First, let's find the total length of fish:

"three 2-in. goldfish, five 1-in. guppies, and a 3-in. loach"

3 × 2 in. + 5 × 1 in. + 3 in. = 6 in. + 5 in. + 3 in. = 14 in.

The total length of fish is 14 inches. The graph does not show 14 inches, but we can write an equation of the line of the graph and find the size of tank using 14 inches of length.

y = mx + b

where y = capacity of tank, m = slope, x = total length of fish, b = y-intercept.

From the graph we see that point (0, 4) is on the line, so b = 4

y = mx + 4

To find the slope, we use 2 points on the line: (0, 4), (2, 6)

slope = m = (6 - 4)/(2 - 0) = 2/2 = 1

m = 1, so the equation of the line is
y = x + 4

Now we let x = 14 representing the total length of fish, and we solve for y.

y = 14 + 4

y = 18

y is the capacity of the tank.

Answer: 18 gallons