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.
a=4 and b=5
fish a is 7 inches long
fish b is 5 inches long
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
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
compare, asssuming that all planties are same legnth and all guppies are same legnth
looks like we just added 2p to first euation to get secon equation
guppies are 3 inches
planties are 2 inches