MATH help systems of equations, a fun word problem!

Discus: SAT/ACT Tests and Test Preparation: October 2003 Archive: MATH help systems of equations, a fun word problem!
 By Entropie (Entropie) on Sunday, October 26, 2003 - 01:26 am: Edit

i hate these. heres the question:
In 1990, the aquariums with the greatest attendance were the Sea Worlds in Florida, California, and Texas. The total attendance at these three was 10,200,000. Sea world of Florida had 300,000 more than Sea world of California, Sea World of California had 1,200,000 more than sea world of texas. What was the attendance of each?

i got this so far:
F+C+T=10,200,000
F=C+300,000
C=T+1,200,000 (and solving for T):
T=-1,200,000+C

 By Miseryxsignals (Miseryxsignals) on Sunday, October 26, 2003 - 02:10 am: Edit

well for the convenience of simplicity, take off the last three zeroes of each term. (we'll add them in later)
This is what you have:

F+C+T = 10,200
F=C+300
T=C-1,200

So you have equations of each of the terms with C as a variable, plug those into the first equation:

(C+300)+C=(C-1,200) = 10,200
3C - 900 = 10,200
3C = 11,100
C = 3,700

F = C + 300
F = 3,700 + 300
F = 4,000

T = C-1,200
T = 3,700-1,200
T = 2,500

Then remember to add the zeroes to each term:
C=3,700,000
F=4,000,000
T=2,500,000

Hope this helps. BTW, sometimes taking away 3 zeroes and putting them back later will mess up the problem, but for this specific one its ok.

 By Suchitar (Suchitar) on Sunday, October 26, 2003 - 02:15 am: Edit

good going so far
now, substitute for f and t in the original equation
c+300,000 + c + c-1,200,000=10,200,000

solve for c(c=3,700,000 unless ive made a calculation error)

put c in f=c+300,000 n find f

put c in t=c-1,200,000 and find t

 By Entropie (Entropie) on Sunday, October 26, 2003 - 02:51 am: Edit

ohh yeah, thanks both of you, i was actually leaning towards doing it the way suchitar did it, but i made a fatal mistake and kept going around in circles. Thanks for clearing it up!

 By Entropie (Entropie) on Sunday, October 26, 2003 - 02:55 am: Edit

oh wait, i just found out you both did it the same way >_<

o well