A question abouth fish and math

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 34 gallons of water and Hank's aquarium hold 50 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?

Answer 1

Marta bought 3 of fish A and 2 of fish B, and her tank holds 34 gallons.

So 3A + 2B = 34

Hank bought 3 of fish A and 4 of fish B, with a tank holding 50 gallons.

So, 3A + 4B = 50.

This works really well for both elimination and substitution methods. I like elimination for this one, and you'll see why below.

If we start with Hank's 50 gallon fish tank and moved his 3 As and 2 of his Bs into a tank identical to Marta's, that would be like starting with

3A +4B = 50

-( 3A +2B = 34)

2B = 16

And we'd be left with 2 fish B in 16 gallons of water.

So, One of fish B should be kept in 8 gallons. It's 8 inches long.

Take that answer for B and plug it back into either Marta's or Hank's original equations from earlier to find how many gallons (and how many inches) each of fish A is.