A neighborhood group goes to the movies every Saturday night. Last week, they purchased 29 adult tickets and 17 youth tickets for $$ 254$ . This week they purchased 21 adult tickets and 22 youth tickets for $$ 213$ . Find the cost of one adult ticket.
$$ 7$
$$ 3$
$$ 9$
$$ 6$

Answer

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Answer

Thus, the cost of one adult ticket is $7$ dollars.

Steps

Step 1 ：Let's denote the cost of one adult ticket as 'a' and the cost of one youth ticket as 'y'.

Step 2 ：From the first week's purchase, we can form the equation $29 a + 17 y = 254$ .

Step 3 ：From the second week's purchase, we can form the equation $21 a + 22 y = 213$ .

Step 4 ：These form a system of linear equations that we can solve to find the values of 'a' and 'y'.

Step 5 ：Solving this system, we find that 'a' equals 7 and 'y' equals 3.

Step 6 ：Thus, the cost of one adult ticket is $7$ dollars.