Tickets to a community theater cost \( \$ 35 \) for adults and \( \$ 10 \) for children. At a recent performance, a total of 273 tickets were sold for \( \$ 6830 \). How many tickets for adults were sold?

Step 1 ：Let x be the number of adult tickets and y be the number of child tickets. Then we have two equations:

Step 2 ：35x + 10y = 6830

Step 3 ：x + y = 273

Step 4 ：Isolate x in the second equation: x = 273 - y

Step 5 ：Substitute the expression of x into the first equation: 35(273 - y) + 10y = 6830

Step 6 ：Simplify the equation: -25y = -2780

Step 7 ：Divide both sides by -25: y = 111

Step 8 ：Substitute the value of y into the expression of x: x = 273 - 111 = 162