Linear systems word problems: tickets, money and mixtures

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Learn it Let a variable stand for each unknown amount. Write one equation for the total number of things and another for the total value (or cost, or mass). Then solve the system.

Example: Adult tickets cost $12, child tickets $7. 50 tickets sold for $475.

a + c = 50 and 12a + 7c = 475.
12a + 7(50 − a) = 475 → 5a = 125 → a = 25.
25 adult and 25 child tickets.

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