# 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 24 gallons of water and hanks aquarium hold 42 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 is 4 inches.

Fish B is 5 inches.

Step-by-step explanation:

22=3a+2b

and

32=3a+4b

So,

a=4 and b=5

fish a is 7 inches long

fish b is 5 inches long

Step-by-step explanation:

set up system of equations and use subtraction

Marta's 3a + 2b = 31

Hank's . 3a + 4b = 41

subtract the two equation (make sure you take the negative all the way through the bottom equation

3a cancels with -3a and you are left with

-2b = -10

b = 5

plug b = 5 into one of the equations and solve for a.

We can let the variables A and B stand for the length in inches of fish A and fish B, respectively.

If we assume each person bought fish having a total length of 1 inch per gallon of aquarium, then we can write equations ...

... 3A +2B = 33 . . . . . total length of Marta's fish

... 3A +4B = 45 . . . . . total length of Hank's fish

Subtracting the first equation from the second, we get ...

... 2B = 12

... B = 6 . . . . . divide by 2

Using this value in the first equation, we have ...

... 3A + 2·6 = 33

... 3A = 21 . . . . . . . . subtract 12

... A = 7 . . . . . . . . . . divide by 3

Fish A is 7 inches long; fish B is 6 inches long.

Martha: 3x3= 9 2x2= 4 9+4= 13

Hank: 3x3= 9 4x2= 8 9+8=17

guppylegnth=g

plantielegnth=p

martha has 13 inches of fish

hank has 17 inchs of fish

the amount of fish is calculated by

amount of each fish times legnth of fish

martha:

13=3g+2p

hank:

17=3g+4p

compare, asssuming that all planties are same legnth and all guppies are same legnth

13=3g+2p

17=3g+4p

looks like we just added 2p to first euation to get secon equation

minus them

-13=-3g-2p

17=3g+4p +

4=0g+2p

4=2p

divide 2

2=p

sub back

13=3g+2p

13=3g+2(2)

13=3g+4

minus 4

9=3g

divide 3

3=g

guppies are 3 inches

planties are 2 inches

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