The eighth grade is going on a field trip to the Science Museum, where they will spend the day and see a great 3-D IMAX movie. The museum offers a group price of $189, and the students will each pay an equal part of that total. When rainy weather caused a baseball game to be rescheduled for the day of the field trip 12 of the students had to miss the trip to play in the game. As a result each student who went to the movie paid one dollar more than they would have if the baseball players had gone to. How many students went on the field trip and how much did each one pay?

[tex]Let\ number\ of\ students=x\\\\Group\ price=\$189\\\\Per\ student\ price=\frac{total\ price}{number\ of\ students}\\\\Per\ student\ price=\frac{189}{x}\\\\When\ 12\ students\ missed\ the\ trip\\\\Number\ of\ remaining\ students=x-12\\\\Now\ per\ students\ price=\frac{189}{x-12}\\\\Given\ that\ when\ 12\ students\ missed\ the\ field\ trip\ per\ student\ cost\ increases\ by\ \$ 1.\\\\\frac{189}{x}+1=\frac{189}{x-12}\\\\Multiply\ both\ sides\ by\ x(x-12)[/tex]

[tex]\frac{189x(x-12)}{x}+x(x-12)=\frac{189x(x-12)}{x-12}\\\\189(x-12)+x^2-12x=189x\\\\189x-189\times 12+x^2-12x=189x\\\\x^2-12-2268=0\\\\x^2-54x+42x-2268=0\\\\x(x-54)+42(x-54)=0\\\\(x-54)(x+42)=0\\\\x=54,-42\\\\Number\ of\ students\ can\ not\ be\ negative\\\\Hence\ total\ number\ of\ students=54\\\\Students\ went\ on\ field\ trip=54-12=42\\\\Per\ students\ cost=\frac{189}{42}=\$ 4.5[/tex]