Mathematics
jamie007
34

Tickets to the zoo cost $14 for adults and $10 for children. A group of 12 people went to the zoo, and the tickets cost $140. The system of equations models this situation, where x is the number of adults and y is the number of children. x+y=12 14x+10y=140 How many adults and how many children were in the group? A. 5 adults and 7 children B. 6 adults and 6 children C. 7 adults and 5 children D. 8 adults and 4 children

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(1) Answers
Kip

 x is the number of adults and y is the number of children.    x + y = 12 14x + 10y = 140 lets multiply the first equation by -10 and then add it to the second equation: -10x - 10y = -120 14x + 10y = 140 ----------------------- 4x + 0 = 20 x = 20/4 x = 5 then substitute in the original equation: x + y = 12 5 + y = 12 y = 12 - 5 y = 7 therefore there were 5 adults and 7 children

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