# One evening 1600 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $20 for covered pavilion seats and$15 for lawn seats. Total receipts were $26,000. How many tickets of each type were sold? How many pavilion seats were sold? ##### 1 Answer Nov 17, 2016 There were 400 pavilion tickets sold and 1,200 lawn tickets sold. #### Explanation: Let's call the pavilion seats sold $p$and the lawn seats sold $l$. We know there was a total of 1600 concert tickets sold. Therefore: $p + l = 1600$If we solve for $p$we get $p + l - l = 1600 - 1$$p = 1600 - l$We also know pavilion tickets go for$20 and lawn tickets go for $15 and the total receipts were$26000. Therefore:

$20 p + 15 l = 26000$

Now substituting $1600 - l$ from the first equation into the second equation for $p$ and solving for $l$ while keeping the equation balanced gives:

$20 \left(1600 - l\right) + 15 l = 26000$

$32000 - 20 l + 15 l = 26000$

$32000 - 5 l = 26000$

$32000 - 5 l + 5 l - 26000 = 26000 + 5 l - 26000$

$6000 = 5 l$

$\frac{6000}{5} = \frac{5 l}{5}$

$1200 = l$

Substitute $1200$ for $l$ in the result of the first equation to solve for $p$:

$p = 1600 - 1200$

$p = 400$