Question

The rule for the number of fish in a home aquarium is 1 gallon of water for each inch of fish length. Marta's aquarium holds 31 gallons of water and Hank's aquarium hold 47 gallons of water. The aquarium holds two types of fish, fish A and fish B. If Marta bought 3 of fish A and 2 of fish B, and Hank bought 3 of fish A and 4 of fish B, how long is fish A and how long is fish B? Fish A measure _____ inches in the length, and fish B measures _______ inches in the length

Answer 1

Fish A 5 inches in the length, and fish B measures 8 inches in the length.

Step-by-step explanation

We have that the rule for the number of fish is 1 gallon of water for every inch of fish.

Let the length of fish A be a.

Let the length of fish B be b.

Marta's aquarium holds 31 gallons of water. This means that she can only have 31 inches of fish in her aquarium.

She bought 3 of fish A and 2 of fish B. This means that the total length of fish in her aquarium is:

3a + 2b = 31 ________(1)

Hank's aquarium hold 47 gallons of water. This means that he can only have 47 inches of fish in his aquarium.

He bought 3 of fish A and 4 of fish B. This means that the total length of fish in his aquarium is:

3a + 4b = 47 _________(2)

Now, we have two simultaneous equations:

3a + 2b = 31

3a + 4b = 47

From the second equation, make 3a subject of formula:

3a = 47 - 4b

Substitute that into equation 1:

47 - 4b + 2b = 31

Collect like terms:

-4b + 2b = 31 - 47

-2b = -16

Divide through by -2:

b = -16 / -2

b = 8

Recall that:

3a = 47 - 4b

=> 3a = 47 - 4(8)

3a = 47 - 32

3a = 15

Divide through by 3:

a = 15 / 3

a = 5

Therefore, Fish A 5 inches in the length, and fish B measures 8 inches in the length.