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 13 gallons of water and Hank's aquarium hold 17 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 measures ____ Inches in length, and fish B measures ____ inches in length.

Answer 1

We have

1 gallon of water for each inch of fish

x= Measure fish A

y= Measure fish B

The equation for Martha's Aquarium

3x+2y=13 ....(1)

Equation for Hank's Acuarium

3x+4y=17 ....(2)

We have a system of equations,in order to solve the system we will multiply the second equation by -1

-3x-4y=-17

then we sum the equation above plus the first equation

-2y=-4

y=-4/-2

y=2

then we substitute the value of y into the first equation

3x+2y=13

3x+2(2)=13

3x+4=13

3x=13-4

3x=9

x=9/3

x=3

Fish A measures 3 inches in length, and fish B measures 2 inches in length.​