Please help...these word problems are very humbling for me...
Average movie prices in general are lower in the United States than in other countries. It would cost $81.35 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $77.05. How much does an average movie cost in each of these countries?
I really appreciate your help...thank you...
Word problems are only a matter of translating English sentences into
Algebra sentences.
>>...It would cost $81.35 to buy three tickets in Japan plus two tickets in Switzerland...<<
That English sentence translates into this Algebra sentence:
3J + 2S = 81.35
>>...Three tickets in Switzerland plus two tickets in Japan would cost $77.05....<<
That English sentence translates into this Algebra sentence:
3S + 2J = 77.05
Solve the system of equations:
3J + 2S = 81.35
3S + 2J = 77.05
Reverse the terms on the left of one of the equations so
like letters will line up vertically, so we can solve the
system by elimination rather than substitution.
3J + 2S = 81.35
2J + 3S = 77.05
This is more easily solved by elimination since there is
no term J, -J, S or -S. If there had been, substitution
would have been easier.
Multiply the first equation through by -2 and the second
one through by +3
-6J - 4S = -162.70
6J + 9S = 231.15
------------------
5S = 68.45
S = 13.69
Start over to find J
3J + 2S = 81.35
2J + 3S = 77.05
Multiply the first equation through by -3 and the second
one through by 2
-9J - 6S = -244.05
4J + 6S = 154.10
------------------
-5J = -89.95
J = 17.99
Answer: An average movie ticket costs $17.99 in Japan and $13.69
in Switzerland.
Edwin
