Question

a jazz concert brought in $199,000 on the sale of 7,900 tickets. if the tickets sold for $20 and $30 each, how many of each type of ticket were sold?
the number of $20 tickets is \square.

Explanation:

Step1: Define variables

Let \( x \) be the number of \(\$20\) tickets and \( y \) be the number of \(\$30\) tickets. We know two equations: \( x + y = 7900 \) (total number of tickets) and \( 20x + 30y = 199000 \) (total revenue).

Step2: Solve the first equation for \( y \)

From \( x + y = 7900 \), we get \( y = 7900 - x \).

Step3: Substitute \( y \) into the second equation

Substitute \( y = 7900 - x \) into \( 20x + 30y = 199000 \):
\[

$$\begin{align*} 20x + 30(7900 - x) &= 199000\\ 20x + 237000 - 30x &= 199000\\ -10x &= 199000 - 237000\\ -10x &= -38000\\ x &= \frac{-38000}{-10}\\ x &= 3800 \end{align*}$$

\]

Answer:

3800