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?

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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?

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Answer 1 · 2016-11-17T22:29:06

There were 400 pavilion tickets sold and 1,200 lawn tickets sold.

Explanation:

Let's call the pavilion seats sold $p$ $p$ and the lawn seats sold $l$ $l$ . We know there was a total of 1600 concert tickets sold. Therefore:

$p + l = 1600$ $p + l = 1600$ If we solve for $p$ $p$ we get $p + l - l = 1600 - 1$ $p + l - l = 1600 - 1$

$p = 1600 - l$ $p = 1600 - l$

We also know pavilion tickets go for $20 and lawn tickets go for $15 and the total receipts were $26000. Therefore:

$20 p + 15 l = 26000$ $20p + 15l = 26000$

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

$20 (1600 - l) + 15 l = 26000$ $20(1600 - l) + 15l = 26000$

$32000 - 20 l + 15 l = 26000$ $32000 - 20l + 15l = 26000$

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

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

$6000 = 5 l$ $6000 = 5l$

$\frac{6000}{5} = \frac{5 l}{5}$ $6000/5 = (5l)/5$

$1200 = l$ $1200 = l$

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

$p = 1600 - 1200$ $p = 1600 - 1200$

$p = 400$ $p = 400$

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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

Explanation:

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