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A movie theater made $63 selling 29 tickets. They sell child tickets for $3, adult tickets for $2, and senior tickets for $2. They sold three times as many child tickets as adult tickets. Using c for a child ticket, a for an adult ticket, and s for a senior ticket, what system of equations represents this scenario?

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Answer:This is a "two equations, two unknowns" problem.

First lets find our two equations: Children are C and Adults are A

8.50A + 5.50C = 194.00 .      COST EQUATION

A + C = 26                             TICKETS EQUATION

based on these numbers substitution is the best method (rather than elimination). Since we need both A and C, it doesnt matter which one we do first.

A = 26-C

substituting in the first equation we get

8.5(26-C) + 5.5C = 194

distribute the 8.5

221-8.5C +5.5C = 194

combine like terms and solve for C

221-3C = 194

3C = 27

C = 9                   so we sold 9 childrens tickets

to find the adult we can go back to our original second equation

A + C = 26 TICKETS EQUATION

subbing in 9 for C

we get A = 17

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