another fun math question!! :D?

Question

hahaha i love these! This time, try to solve using Matrices! :

In 1990, the aquariums with the greatest attendence were the sea Worlds in Florida, California, and texas. The total attendance for all three was 10.2 million. Sea World of Florida had 0.3 million more than Sea World of California. Sea World of Cailfornia had 1.2 million more than Sea World of Texas. What was the 1990 attendance of each?

Answer 1

F + C + T = 10.2
F - C = 0.3
C - T = 1.2

If you want to do this by matrices, set up the equation like this

Ax = b

| 1 1 1| | F |....|10.2|
|1 -1 0| | C| = | 0.3 |
|0 1 -1| | T |....| 1.2 |

If you premulyiply by A^-1

A^-1Ax = A^-1b

x = A^-1 b

| 1/3 2/3 1/3 |
|1/3 -1/3 1/3 | = A^-1
|1/3 -1/3 -2/3|

| 1/3 2/3 1/3 | |10.2|....| 4.0 |
|1/3 -1/3 1/3 | | 0.3 | = | 3.7 |
|1/3 -1/3 -2/3| | 1.2 |....| 2.5 |

So F = 4.0 million, C = 3.7 million and T = 2.5 million.

Answer 2

Let the attendence in
Florida =x
California = y
Texas = z
x+y+z=10.2 -- (1)
x=y+0.3 -- (2) means y=0.3-x
y=z+1.2 -- (3) means z=1.2-y = 1.2-(0.3-x)
go to (1)
x+(0.3-x)+1.2-0.3+x=10.2
1.2+x=10.2
x=10.2-1.2=9 million (Florida)
using (2) y=0.3-9
The results (equations)are inconsistent. You're getting negative number of people. You do not need matrices to solve this problem.

Answer 3

x + y + z = 10.2 million

x = Florida
y= California
z = Texas

x = y+0.3
y = z + 1.2
z = y - 1.2

x + y + z = 10.2
y + 0.3 + y + y - 1.2 = 10.2
3y - 0.9 = 10.2
y - 0.3 = 3.4
y = 3.7

California = 3.7 million
Florida = 4 million
Texas = 2.5 million

3.7 + 4 + 2.5 = 10.2

Answer 4

F=florida
T=texas
C=california...

set up your equations...

F+T+C=10.2
F=0.3+C
C=1.2+T

you have 3 equations...and 3 unknowns... solve for F in the second one, T in the 3rd one...
plug those into the first one and you can find out what C is. then go back to those last 2 equations and solve for both F and T.

Answer 5

x = amount Texas
x+ 1.2 = amount California
x+ 1.5 = amount Florida
3x+2.7 = 10.2
3x = 7.5
x = 2.5 million for Texas
x+ 1.2 = 3.7 million for California
x + 1.5 = 4 million fo Florida