Question

A 1300-seat theater sells two types of tickets for a concert. Premium seats sell for $30 each and regular seats sell for $20 each. At one event S31,820 was
collected in ticket sales with 20 seats left unsold. How many of each type of ticket was sold?

Answer 1

A  theater sells two types of tickets for a concert premium seats and regular seats . They sold,

622  premium seats sold

658 regular seats sold

Given :

Premium seats sell for $30 each and regular seats sell for $20 each.

Total of 1300 seat with 20 seats left unsold.

Total collection is 31,820

Let x be number of premium seats sold

and y be the number of regular seats sold

Total of 1300 seat with 20 seats left unsold. So,$1300-20= 1280$ seats sold

$x+y= 1280$

Premium seats sell for $30 each and regular seats sell for $20 each. Total collection is 31,820

$30x+20y=31820$

Now we solve for x  and y

$x+y=1280\\x=1280-y$

Substitute it in second equation

$30x+20y=31820\\30\left(1280-y\right)+20y=31820\\38400-10y=31820\\38400-10y-38400=31820-38400\\-10y=-6580\\\\\frac{-10y}{-10}=\frac{-6580}{-10}\\y=658$

Now we find out x

$x=1280-y\\x=1280-658\\x=622$

622  premium seats sold

658 regular seats sold

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