One hundred and twenty people attended a musical. The total amount of money collected for tickets was $ 1515. Prices were $ 15 for rices were regular adult admission, $ 12 for children, and $ 10 for senior citizens. Twice as many children's tickets as regular adult tickets were sold. Write a system of equations to find the number of children, adults, and senior citizens that attended the musical. Then solve the system by using a matrix equation and the inverse matrix.

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